LMFDB - Embedded newform 38.9.d.a.27.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,9,Mod(27,38)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("38.27");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	38.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.4803871823$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.7
Character	$\chi$	$=$	38.27
Dual form			38.9.d.a.31.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.79796 + 5.65685i) q^{2} +(-107.051 - 61.8057i) q^{3} +(64.0000 + 110.851i) q^{4} +(333.136 - 577.008i) q^{5} +(-699.252 - 1211.14i) q^{6} -377.866 q^{7} +1448.15i q^{8} +(4359.40 + 7550.70i) q^{9} +O(q^{10})$	\(q+(9.79796 + 5.65685i) q^{2} +(-107.051 - 61.8057i) q^{3} +(64.0000 + 110.851i) q^{4} +(333.136 - 577.008i) q^{5} +(-699.252 - 1211.14i) q^{6} -377.866 q^{7} +1448.15i q^{8} +(4359.40 + 7550.70i) q^{9} +(6528.10 - 3769.00i) q^{10} -7604.40 q^{11} -15822.3i q^{12} +(-15498.5 + 8948.07i) q^{13} +(-3702.31 - 2137.53i) q^{14} +(-71324.8 + 41179.4i) q^{15} +(-8192.00 + 14189.0i) q^{16} +(-61731.2 + 106922. i) q^{17} +98641.9i q^{18} +(-120460. + 49728.5i) q^{19} +85282.7 q^{20} +(40450.8 + 23354.3i) q^{21} +(-74507.6 - 43017.0i) q^{22} +(-72363.6 - 125337. i) q^{23} +(89504.3 - 155026. i) q^{24} +(-26646.1 - 46152.3i) q^{25} -202472. q^{26} -266728. i q^{27} +(-24183.4 - 41886.9i) q^{28} +(131930. - 76169.7i) q^{29} -931783. q^{30} -211602. i q^{31} +(-160530. + 92681.9i) q^{32} +(814056. + 469996. i) q^{33} +(-1.20968e6 + 698409. i) q^{34} +(-125881. + 218031. i) q^{35} +(-558003. + 966490. i) q^{36} +3.04646e6i q^{37} +(-1.46157e6 - 194188. i) q^{38} +2.21217e6 q^{39} +(835596. + 482432. i) q^{40} +(-1.11473e6 - 643591. i) q^{41} +(264223. + 457649. i) q^{42} +(754096. - 1.30613e6i) q^{43} +(-486682. - 842958. i) q^{44} +5.80908e6 q^{45} -1.63740e6i q^{46} +(-2.82350e6 - 4.89045e6i) q^{47} +(1.75392e6 - 1.01263e6i) q^{48} -5.62202e6 q^{49} -602932. i q^{50} +(1.32167e7 - 7.63068e6i) q^{51} +(-1.98381e6 - 1.14535e6i) q^{52} +(9.50811e6 - 5.48951e6i) q^{53} +(1.50884e6 - 2.61339e6i) q^{54} +(-2.53330e6 + 4.38780e6i) q^{55} -547208. i q^{56} +(1.59688e7 + 2.12166e6i) q^{57} +1.72352e6 q^{58} +(-8.35876e6 - 4.82593e6i) q^{59} +(-9.12957e6 - 5.27096e6i) q^{60} +(7.02107e6 + 1.21608e7i) q^{61} +(1.19700e6 - 2.07327e6i) q^{62} +(-1.64727e6 - 2.85315e6i) q^{63} -2.09715e6 q^{64} +1.19237e7i q^{65} +(5.31739e6 + 9.21000e6i) q^{66} +(-2.98271e7 + 1.72207e7i) q^{67} -1.58032e7 q^{68} +1.78899e7i q^{69} +(-2.46674e6 + 1.42418e6i) q^{70} +(-5.30319e6 - 3.06180e6i) q^{71} +(-1.09346e7 + 6.31308e6i) q^{72} +(2.72872e7 - 4.72629e7i) q^{73} +(-1.72334e7 + 2.98491e7i) q^{74} +6.58752e6i q^{75} +(-1.32219e7 - 1.01705e7i) q^{76} +2.87344e6 q^{77} +(2.16747e7 + 1.25139e7i) q^{78} +(-5.50960e7 - 3.18097e7i) q^{79} +(5.45809e6 + 9.45369e6i) q^{80} +(1.21167e7 - 2.09867e7i) q^{81} +(-7.28141e6 - 1.26118e7i) q^{82} -1.25546e7 q^{83} +5.97870e6i q^{84} +(4.11297e7 + 7.12387e7i) q^{85} +(1.47772e7 - 8.53163e6i) q^{86} -1.88309e7 q^{87} -1.10124e7i q^{88} +(-8.39613e7 + 4.84751e7i) q^{89} +(5.69171e7 + 3.28611e7i) q^{90} +(5.85636e6 - 3.38117e6i) q^{91} +(9.26254e6 - 1.60432e7i) q^{92} +(-1.30782e7 + 2.26521e7i) q^{93} -6.38886e7i q^{94} +(-1.14359e7 + 8.60727e7i) q^{95} +2.29131e7 q^{96} +(-6.41775e7 - 3.70529e7i) q^{97} +(-5.50843e7 - 3.18029e7i) q^{98} +(-3.31506e7 - 5.74186e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 168 q^{3} + 1536 q^{4} - 558 q^{5} + 896 q^{6} + 11992 q^{7} + 18448 q^{9}+O(q^{10}) $ 24 * q + 168 * q^3 + 1536 * q^4 - 558 * q^5 + 896 * q^6 + 11992 * q^7 + 18448 * q^9	\( 24 q + 168 q^{3} + 1536 q^{4} - 558 q^{5} + 896 q^{6} + 11992 q^{7} + 18448 q^{9} + 33516 q^{11} + 60870 q^{13} - 71424 q^{14} - 351930 q^{15} - 196608 q^{16} + 3546 q^{17} - 727738 q^{19} - 142848 q^{20} - 674568 q^{21} - 681600 q^{22} + 726 q^{23} - 114688 q^{24} - 277874 q^{25} - 960000 q^{26} + 767488 q^{28} - 254286 q^{29} - 71168 q^{30} - 2796150 q^{33} - 2740224 q^{34} - 690672 q^{35} - 2361344 q^{36} - 6829056 q^{38} - 1599924 q^{39} - 5153976 q^{41} + 4153600 q^{42} + 5692338 q^{43} + 2145024 q^{44} + 42653840 q^{45} + 11113938 q^{47} - 2752512 q^{48} + 17359944 q^{49} + 62169786 q^{51} + 7791360 q^{52} + 10399050 q^{53} - 24215680 q^{54} + 40181572 q^{55} - 27798558 q^{57} - 10126848 q^{58} - 58809492 q^{59} - 45047040 q^{60} - 45012614 q^{61} + 5892096 q^{62} + 62488724 q^{63} - 50331648 q^{64} + 45107968 q^{66} - 93677268 q^{67} + 907776 q^{68} - 291840 q^{70} + 5993046 q^{71} + 11698176 q^{72} + 23359860 q^{73} - 31474944 q^{74} - 1303552 q^{76} + 35611680 q^{77} + 94099200 q^{78} - 93221166 q^{79} - 9142272 q^{80} - 115510580 q^{81} + 6074880 q^{82} - 194283156 q^{83} - 15300674 q^{85} + 58611456 q^{86} + 89779380 q^{87} - 49833126 q^{89} - 63377664 q^{90} - 101275308 q^{91} - 92928 q^{92} - 157549992 q^{93} - 87570126 q^{95} - 29360128 q^{96} - 178814556 q^{97} - 88409088 q^{98} - 54444376 q^{99}+O(q^{100}) \) 24 * q + 168 * q^3 + 1536 * q^4 - 558 * q^5 + 896 * q^6 + 11992 * q^7 + 18448 * q^9 + 33516 * q^11 + 60870 * q^13 - 71424 * q^14 - 351930 * q^15 - 196608 * q^16 + 3546 * q^17 - 727738 * q^19 - 142848 * q^20 - 674568 * q^21 - 681600 * q^22 + 726 * q^23 - 114688 * q^24 - 277874 * q^25 - 960000 * q^26 + 767488 * q^28 - 254286 * q^29 - 71168 * q^30 - 2796150 * q^33 - 2740224 * q^34 - 690672 * q^35 - 2361344 * q^36 - 6829056 * q^38 - 1599924 * q^39 - 5153976 * q^41 + 4153600 * q^42 + 5692338 * q^43 + 2145024 * q^44 + 42653840 * q^45 + 11113938 * q^47 - 2752512 * q^48 + 17359944 * q^49 + 62169786 * q^51 + 7791360 * q^52 + 10399050 * q^53 - 24215680 * q^54 + 40181572 * q^55 - 27798558 * q^57 - 10126848 * q^58 - 58809492 * q^59 - 45047040 * q^60 - 45012614 * q^61 + 5892096 * q^62 + 62488724 * q^63 - 50331648 * q^64 + 45107968 * q^66 - 93677268 * q^67 + 907776 * q^68 - 291840 * q^70 + 5993046 * q^71 + 11698176 * q^72 + 23359860 * q^73 - 31474944 * q^74 - 1303552 * q^76 + 35611680 * q^77 + 94099200 * q^78 - 93221166 * q^79 - 9142272 * q^80 - 115510580 * q^81 + 6074880 * q^82 - 194283156 * q^83 - 15300674 * q^85 + 58611456 * q^86 + 89779380 * q^87 - 49833126 * q^89 - 63377664 * q^90 - 101275308 * q^91 - 92928 * q^92 - 157549992 * q^93 - 87570126 * q^95 - 29360128 * q^96 - 178814556 * q^97 - 88409088 * q^98 - 54444376 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	9.79796	+	5.65685i	0.612372	+	0.353553i
$2$	9.79796	+	5.65685i	0.612372	+	0.353553i
$3$	−107.051	−	61.8057i	−1.32161	−	0.763034i	−0.337627	−	0.941280i	$-0.609624\pi$
$3$	−107.051	−	61.8057i	−1.32161	−	0.763034i	−0.983986	+	0.178246i	$0.942958\pi$
$4$	64.0000	+	110.851i	0.250000	+	0.433013i
$5$	333.136	−	577.008i	0.533017	−	0.923212i	−0.466240	−	0.884658i	$-0.654392\pi$
$5$	333.136	−	577.008i	0.533017	−	0.923212i	0.999257	−	0.0385538i	$-0.0122751\pi$
$6$	−699.252	−	1211.14i	−0.539546	−	0.934522i
$7$	−377.866			−0.157379			−0.0786893	−	0.996899i	$-0.525073\pi$
$7$	−377.866			−0.157379			−0.0786893	+	0.996899i	$0.525073\pi$
$8$			1448.15i			0.353553i
$9$	4359.40	+	7550.70i	0.664441	+	1.15085i
$10$	6528.10	−	3769.00i	0.652810	−	0.376900i
$11$	−7604.40			−0.519391			−0.259695	−	0.965691i	$-0.583622\pi$
$11$	−7604.40			−0.519391			−0.259695	+	0.965691i	$0.583622\pi$
$12$		−	15822.3i		−	0.763034i
$13$	−15498.5	+	8948.07i	−0.542646	+	0.313297i	−0.746151	−	0.665777i	$-0.768100\pi$
$13$	−15498.5	+	8948.07i	−0.542646	+	0.313297i	0.203505	+	0.979074i	$0.434767\pi$
$14$	−3702.31	−	2137.53i	−0.0963743	−	0.0556417i
$15$	−71324.8	+	41179.4i	−1.40888	+	0.813420i
$16$	−8192.00	+	14189.0i	−0.125000	+	0.216506i
$17$	−61731.2	+	106922.i	−0.739110	+	1.28018i	0.213787	+	0.976880i	$0.431420\pi$
$17$	−61731.2	+	106922.i	−0.739110	+	1.28018i	−0.952897	+	0.303295i	$0.901913\pi$
$18$			98641.9i			0.939662i
$19$	−120460.	+	49728.5i	−0.924334	+	0.381584i
$19$	−120460.	+	49728.5i	−0.924334	+	0.381584i
$20$	85282.7			0.533017
$21$	40450.8	+	23354.3i	0.207994	+	0.120085i
$22$	−74507.6	−	43017.0i	−0.318061	−	0.183632i
$23$	−72363.6	−	125337.i	−0.258588	−	0.447888i	0.707276	−	0.706938i	$-0.249924\pi$
$23$	−72363.6	−	125337.i	−0.258588	−	0.447888i	−0.965864	+	0.259050i	$0.916591\pi$
$24$	89504.3	−	155026.i	0.269773	−	0.467261i
$25$	−26646.1	−	46152.3i	−0.0682139	−	0.118150i
$26$	−202472.			−0.443069
$27$		−	266728.i		−	0.501897i
$28$	−24183.4	−	41886.9i	−0.0393446	−	0.0681469i
$29$	131930.	−	76169.7i	0.186531	−	0.107694i	−0.403827	−	0.914836i	$-0.632320\pi$
$29$	131930.	−	76169.7i	0.186531	−	0.107694i	0.590358	+	0.807142i	$0.298987\pi$
$30$	−931783.			−1.15035
$31$		−	211602.i		−	0.229125i	−0.993416	−	0.114563i	$-0.963453\pi$
$31$		−	211602.i		−	0.229125i	0.993416	−	0.114563i	$-0.0365466\pi$
$32$	−160530.	+	92681.9i	−0.153093	+	0.0883883i
$33$	814056.	+	469996.i	0.686434	+	0.396313i
$34$	−1.20968e6	+	698409.i	−0.905221	+	0.522630i
$35$	−125881.	+	218031.i	−0.0838854	+	0.145294i
$36$	−558003.	+	966490.i	−0.332221	+	0.575423i
$37$			3.04646e6i			1.62551i	0.582608	+	0.812753i	$0.302032\pi$
$37$			3.04646e6i			1.62551i	−0.582608	+	0.812753i	$0.697968\pi$
$38$	−1.46157e6	−	194188.i	−0.700947	−	0.0931297i
$39$	2.21217e6			0.956224
$40$	835596.	+	482432.i	0.326405	+	0.188450i
$41$	−1.11473e6	−	643591.i	−0.394489	−	0.227759i	0.289614	−	0.957144i	$-0.406473\pi$
$41$	−1.11473e6	−	643591.i	−0.394489	−	0.227759i	−0.684104	+	0.729385i	$0.739806\pi$
$42$	264223.	+	457649.i	0.0849130	+	0.147074i
$43$	754096.	−	1.30613e6i	0.220573	−	0.382044i	−0.734409	−	0.678707i	$-0.762540\pi$
$43$	754096.	−	1.30613e6i	0.220573	−	0.382044i	0.954982	+	0.296663i	$0.0958738\pi$
$44$	−486682.	−	842958.i	−0.129848	−	0.224903i
$45$	5.80908e6			1.41663
$46$		−	1.63740e6i		−	0.365699i
$47$	−2.82350e6	−	4.89045e6i	−0.578625	−	1.00221i	−0.995637	−	0.0933068i	$-0.970256\pi$
$47$	−2.82350e6	−	4.89045e6i	−0.578625	−	1.00221i	0.417013	−	0.908901i	$-0.363077\pi$
$48$	1.75392e6	−	1.01263e6i	0.330403	−	0.190758i
$49$	−5.62202e6			−0.975232
$50$		−	602932.i		−	0.0964691i
$51$	1.32167e7	−	7.63068e6i	1.95363	−	1.12793i
$52$	−1.98381e6	−	1.14535e6i	−0.271323	−	0.156648i
$53$	9.50811e6	−	5.48951e6i	1.20501	−	0.695713i	0.243346	−	0.969940i	$-0.421755\pi$
$53$	9.50811e6	−	5.48951e6i	1.20501	−	0.695713i	0.961665	+	0.274226i	$0.0884218\pi$
$54$	1.50884e6	−	2.61339e6i	0.177447	−	0.307348i
$55$	−2.53330e6	+	4.38780e6i	−0.276844	+	0.479508i
$56$		−	547208.i		−	0.0556417i
$57$	1.59688e7	+	2.12166e6i	1.51277	+	0.200991i
$58$	1.72352e6			0.152302
$59$	−8.35876e6	−	4.82593e6i	−0.689817	−	0.398266i	0.113727	−	0.993512i	$-0.463721\pi$
$59$	−8.35876e6	−	4.82593e6i	−0.689817	−	0.398266i	−0.803543	+	0.595246i	$0.797055\pi$
$60$	−9.12957e6	−	5.27096e6i	−0.704442	−	0.406710i
$61$	7.02107e6	+	1.21608e7i	0.507088	+	0.878303i	0.999966	+	0.00820450i	$0.00261160\pi$
$61$	7.02107e6	+	1.21608e7i	0.507088	+	0.878303i	−0.492878	+	0.870099i	$0.664055\pi$
$62$	1.19700e6	−	2.07327e6i	0.0810080	−	0.140310i
$63$	−1.64727e6	−	2.85315e6i	−0.104569	−	0.181118i
$64$	−2.09715e6			−0.125000
$65$			1.19237e7i			0.667970i
$66$	5.31739e6	+	9.21000e6i	0.280235	+	0.485382i
$67$	−2.98271e7	+	1.72207e7i	−1.48017	+	0.854576i	−0.999748	−	0.0224611i	$-0.992850\pi$
$67$	−2.98271e7	+	1.72207e7i	−1.48017	+	0.854576i	−0.480422	+	0.877037i	$0.659516\pi$
$68$	−1.58032e7			−0.739110
$69$			1.78899e7i			0.789246i
$70$	−2.46674e6	+	1.42418e6i	−0.102738	+	0.0593159i
$71$	−5.30319e6	−	3.06180e6i	−0.208691	−	0.120488i	0.392012	−	0.919960i	$-0.371779\pi$
$71$	−5.30319e6	−	3.06180e6i	−0.208691	−	0.120488i	−0.600703	+	0.799472i	$0.705113\pi$
$72$	−1.09346e7	+	6.31308e6i	−0.406885	+	0.234915i
$73$	2.72872e7	−	4.72629e7i	0.960878	−	1.66429i	0.240573	−	0.970631i	$-0.422665\pi$
$73$	2.72872e7	−	4.72629e7i	0.960878	−	1.66429i	0.720304	−	0.693658i	$-0.244002\pi$
$74$	−1.72334e7	+	2.98491e7i	−0.574703	+	0.995416i
$75$			6.58752e6i			0.208198i
$76$	−1.32219e7	−	1.01705e7i	−0.396314	−	0.304852i
$77$	2.87344e6			0.0817410
$78$	2.16747e7	+	1.25139e7i	0.585565	+	0.338076i
$79$	−5.50960e7	−	3.18097e7i	−1.41453	−	0.816679i	−0.418718	−	0.908116i	$-0.637521\pi$
$79$	−5.50960e7	−	3.18097e7i	−1.41453	−	0.816679i	−0.995811	+	0.0914373i	$0.970854\pi$
$80$	5.45809e6	+	9.45369e6i	0.133254	+	0.230803i
$81$	1.21167e7	−	2.09867e7i	0.281477	−	0.487533i
$82$	−7.28141e6	−	1.26118e7i	−0.161050	−	0.278946i
$83$	−1.25546e7			−0.264540			−0.132270	−	0.991214i	$-0.542227\pi$
$83$	−1.25546e7			−0.264540			−0.132270	+	0.991214i	$0.542227\pi$
$84$			5.97870e6i			0.120085i
$85$	4.11297e7	+	7.12387e7i	0.787916	+	1.36471i
$86$	1.47772e7	−	8.53163e6i	0.270146	−	0.155969i
$87$	−1.88309e7			−0.328696
$88$		−	1.10124e7i		−	0.183632i
$89$	−8.39613e7	+	4.84751e7i	−1.33819	+	0.772606i	−0.986539	−	0.163524i	$-0.947714\pi$
$89$	−8.39613e7	+	4.84751e7i	−1.33819	+	0.772606i	−0.351654	+	0.936130i	$0.614381\pi$
$90$	5.69171e7	+	3.28611e7i	0.867507	+	0.500856i
$91$	5.85636e6	−	3.38117e6i	0.0854008	−	0.0493062i
$92$	9.26254e6	−	1.60432e7i	0.129294	−	0.223944i
$93$	−1.30782e7	+	2.26521e7i	−0.174830	+	0.302815i
$94$		−	6.38886e7i		−	0.818299i
$95$	−1.14359e7	+	8.60727e7i	−0.140402	+	1.05675i
$96$	2.29131e7			0.269773
$97$	−6.41775e7	−	3.70529e7i	−0.724930	−	0.418539i	0.0916345	−	0.995793i	$-0.470791\pi$
$97$	−6.41775e7	−	3.70529e7i	−0.724930	−	0.418539i	−0.816565	+	0.577254i	$0.804124\pi$
$98$	−5.50843e7	−	3.18029e7i	−0.597205	−	0.344797i
$99$	−3.31506e7	−	5.74186e7i	−0.345105	−	0.597739i
$100$	3.41070e6	−	5.90750e6i	0.0341070	−	0.0590750i
$101$	−6.28349e7	−	1.08833e8i	−0.603831	−	1.04587i	−0.992235	−	0.124377i	$-0.960307\pi$
$101$	−6.28349e7	−	1.08833e8i	−0.603831	−	1.04587i	0.388404	−	0.921489i	$-0.373027\pi$
$102$	1.72663e8			1.59514
$103$			5.25293e7i			0.466716i	0.972391	+	0.233358i	$0.0749714\pi$
$103$			5.25293e7i			0.466716i	−0.972391	+	0.233358i	$0.925029\pi$
$104$	−1.29582e7	−	2.24442e7i	−0.110767	−	0.191854i
$105$	2.69512e7	−	1.55603e7i	0.221728	−	0.128015i
$106$	1.24213e8			0.983887
$107$			3.79820e7i			0.289763i	0.989449	+	0.144881i	$0.0462800\pi$
$107$			3.79820e7i			0.289763i	−0.989449	+	0.144881i	$0.953720\pi$
$108$	2.95672e7	−	1.70706e7i	0.217328	−	0.125474i
$109$	1.82239e8	+	1.05216e8i	1.29103	+	0.745375i	0.978836	−	0.204645i	$-0.0656039\pi$
$109$	1.82239e8	+	1.05216e8i	1.29103	+	0.745375i	0.312191	+	0.950019i	$0.398937\pi$
$110$	−4.96423e7	+	2.86610e7i	−0.339063	+	0.195758i
$111$	1.88289e8	−	3.26126e8i	1.24032	−	2.14829i
$112$	3.09548e6	−	5.36152e6i	0.0196723	−	0.0340735i
$113$			4.68856e7i			0.287558i	0.989610	+	0.143779i	$0.0459255\pi$
$113$			4.68856e7i			0.287558i	−0.989610	+	0.143779i	$0.954074\pi$
$114$	1.44460e8	+	1.11121e8i	0.855320	+	0.657928i
$115$	−9.64276e7			−0.551328
$116$	1.68870e7	+	9.74972e6i	0.0932655	+	0.0538468i
$117$	−1.35128e8	−	7.80164e7i	−0.721113	−	0.416335i
$118$	−5.45992e7	−	9.45686e7i	−0.281617	−	0.487774i
$119$	2.33261e7	−	4.04020e7i	0.116320	−	0.201472i
$120$	−5.96341e7	−	1.03289e8i	−0.287587	−	0.498116i
$121$	−1.56532e8			−0.730233
$122$			1.58869e8i			0.717131i
$123$	7.95553e7	+	1.37794e8i	0.347575	+	0.602018i
$124$	2.34563e7	−	1.35425e7i	0.0992141	−	0.0572813i
$125$	2.24755e8			0.920597
$126$		−	3.72734e7i		−	0.147883i
$127$	2.28797e8	−	1.32096e8i	0.879498	−	0.507778i	0.00900498	−	0.999959i	$-0.497134\pi$
$127$	2.28797e8	−	1.32096e8i	0.879498	−	0.507778i	0.870493	+	0.492181i	$0.163800\pi$
$128$	−2.05478e7	−	1.18633e7i	−0.0765466	−	0.0441942i
$129$	−1.61453e8	+	9.32150e7i	−0.583025	+	0.336610i
$130$	−6.74505e7	+	1.16828e8i	−0.236163	+	0.409046i
$131$	−3.58062e6	+	6.20181e6i	−0.0121583	+	0.0210588i	−0.872041	−	0.489434i	$-0.837204\pi$
$131$	−3.58062e6	+	6.20181e6i	−0.0121583	+	0.0210588i	0.859882	+	0.510492i	$0.170537\pi$
$132$			1.20319e8i			0.396313i
$133$	4.55178e7	−	1.87907e7i	0.145470	−	0.0600532i
$134$	−3.89659e8			−1.20855
$135$	−1.53904e8	−	8.88567e7i	−0.463357	−	0.267519i
$136$	−1.54839e8	−	8.93963e7i	−0.452610	−	0.261315i
$137$	9.58807e7	+	1.66070e8i	0.272176	+	0.471422i	0.969419	−	0.245413i	$-0.0789235\pi$
$137$	9.58807e7	+	1.66070e8i	0.272176	+	0.471422i	−0.697243	+	0.716835i	$0.745590\pi$
$138$	−1.01201e8	+	1.75285e8i	−0.279041	+	0.483313i
$139$	−1.82585e8	−	3.16247e8i	−0.489111	−	0.847164i	0.510811	−	0.859693i	$-0.329345\pi$
$139$	−1.82585e8	−	3.16247e8i	−0.489111	−	0.847164i	−0.999922	+	0.0125288i	$0.996012\pi$
$140$	−3.22254e7			−0.0838854
$141$			6.98035e8i			1.76604i
$142$	−3.46403e7	−	5.99988e7i	−0.0851978	−	0.147567i
$143$	1.17857e8	−	6.80447e7i	0.281845	−	0.162724i
$144$	−1.42849e8			−0.332221
$145$		−	1.01499e8i		−	0.229610i
$146$	5.34718e8	−	3.08720e8i	1.17683	−	0.679443i
$147$	6.01841e8	+	3.47473e8i	1.28888	+	0.744135i
$148$	−3.37704e8	+	1.94974e8i	−0.703865	+	0.406377i
$149$	1.23628e8	−	2.14130e8i	0.250826	−	0.434443i	−0.712928	−	0.701238i	$-0.752631\pi$
$149$	1.23628e8	−	2.14130e8i	0.250826	−	0.434443i	0.963753	+	0.266795i	$0.0859645\pi$
$150$	−3.72646e7	+	6.45442e7i	−0.0736091	+	0.127495i
$151$			4.69409e8i			0.902908i	0.892294	+	0.451454i	$0.149095\pi$
$151$			4.69409e8i			0.902908i	−0.892294	+	0.451454i	$0.850905\pi$
$152$	−7.20145e7	−	1.74445e8i	−0.134910	−	0.326801i
$153$	−1.07644e9			−1.96438
$154$	2.81539e7	+	1.62547e7i	0.0500559	+	0.0288998i
$155$	−1.22096e8	−	7.04921e7i	−0.211531	−	0.122128i
$156$	1.41579e8	+	2.45222e8i	0.239056	+	0.414057i
$157$	3.42942e8	−	5.93993e8i	0.564445	−	0.977648i	−0.432656	−	0.901559i	$-0.642423\pi$
$157$	3.42942e8	−	5.93993e8i	0.564445	−	0.977648i	0.997101	−	0.0760889i	$-0.0242433\pi$
$158$	−3.59886e8	−	6.23340e8i	−0.577479	−	1.00022i
$159$	−1.35713e9			−2.12341
$160$			1.23503e8i			0.188450i
$161$	2.73437e7	+	4.73607e7i	0.0406962	+	0.0704880i
$162$	2.37437e8	−	1.37084e8i	0.344738	−	0.199034i
$163$	6.69103e8			0.947857			0.473928	−	0.880563i	$-0.342836\pi$
$163$	6.69103e8			0.947857			0.473928	+	0.880563i	$0.342836\pi$
$164$		−	1.64759e8i		−	0.227759i
$165$	5.42382e8	−	3.13145e8i	0.731762	−	0.422483i
$166$	−1.23010e8	−	7.10198e7i	−0.161997	−	0.0935291i
$167$	5.72321e8	−	3.30430e8i	0.735823	−	0.424828i	−0.0847254	−	0.996404i	$-0.527001\pi$
$167$	5.72321e8	−	3.30430e8i	0.735823	−	0.424828i	0.820549	+	0.571576i	$0.193668\pi$
$168$	−3.38206e7	+	5.85790e7i	−0.0424565	+	0.0735368i
$169$	−2.47729e8	+	4.29080e8i	−0.303690	+	0.526007i
$170$			9.30659e8i			1.11428i
$171$	−9.00618e8	−	6.92772e8i	−1.05331	−	0.810226i
$172$	1.93049e8			0.220573
$173$	8.49535e8	+	4.90479e8i	0.948411	+	0.547566i	0.892587	−	0.450875i	$-0.148888\pi$
$173$	8.49535e8	+	4.90479e8i	0.948411	+	0.547566i	0.0558244	+	0.998441i	$0.482221\pi$
$174$	−1.84504e8	−	1.06524e8i	−0.201284	−	0.116211i
$175$	1.00686e7	+	1.74394e7i	0.0107354	+	0.0185943i
$176$	6.22953e7	−	1.07899e8i	0.0649239	−	0.112451i
$177$	5.96541e8	+	1.03324e9i	0.607781	+	1.05271i
$178$	−1.09687e9			−1.09263
$179$			1.72060e9i			1.67597i	0.545690	+	0.837987i	$0.316268\pi$
$179$			1.72060e9i			1.67597i	−0.545690	+	0.837987i	$0.683732\pi$
$180$	3.71781e8	+	6.43944e8i	0.354158	+	0.613420i
$181$	−6.59400e8	+	3.80705e8i	−0.614377	+	0.354711i	−0.774677	−	0.632358i	$-0.782087\pi$
$181$	−6.59400e8	+	3.80705e8i	−0.614377	+	0.354711i	0.160300	+	0.987068i	$0.448754\pi$
$182$	7.65072e7			0.0697295
$183$		−	1.73577e9i		−	1.54770i
$184$	1.81508e8	−	1.04794e8i	0.158352	−	0.0914248i
$185$	1.75783e9	+	1.01488e9i	1.50069	+	0.866422i
$186$	−2.56280e8	+	1.47963e8i	−0.214122	+	0.123624i
$187$	4.69429e8	−	8.13075e8i	0.383887	−	0.664912i
$188$	3.61409e8	−	6.25978e8i	0.289312	−	0.501104i
$189$			1.00788e8i			0.0789877i
$190$	−5.98949e8	+	7.78646e8i	−0.459595	+	0.597483i
$191$	−7.73939e8			−0.581532			−0.290766	−	0.956794i	$-0.593910\pi$
$191$	−7.73939e8			−0.581532			−0.290766	+	0.956794i	$0.593910\pi$
$192$	2.24502e8	+	1.29616e8i	0.165202	+	0.0953792i
$193$	−1.14819e9	−	6.62910e8i	−0.827534	−	0.477777i	0.0254735	−	0.999675i	$-0.491891\pi$
$193$	−1.14819e9	−	6.62910e8i	−0.827534	−	0.477777i	−0.853008	+	0.521898i	$0.825224\pi$
$194$	−4.19206e8	−	7.26086e8i	−0.295951	−	0.512603i
$195$	7.36952e8	−	1.27644e9i	0.509684	−	0.882798i
$196$	−3.59809e8	−	6.23208e8i	−0.243808	−	0.422288i
$197$	1.70244e9			1.13033			0.565166	−	0.824977i	$-0.308812\pi$
$197$	1.70244e9			1.13033			0.565166	+	0.824977i	$0.308812\pi$
$198$		−	7.50113e8i		−	0.488052i
$199$	−1.48233e9	−	2.56748e9i	−0.945222	−	1.63717i	−0.755306	−	0.655372i	$-0.772512\pi$
$199$	−1.48233e9	−	2.56748e9i	−0.945222	−	1.63717i	−0.189916	−	0.981800i	$-0.560821\pi$
$200$	6.68357e7	−	3.85876e7i	0.0417723	−	0.0241173i
$201$	4.25735e9			2.60828
$202$		−	1.42179e9i		−	0.853946i
$203$	−4.98518e7	+	2.87819e7i	−0.0293560	+	0.0169487i
$204$	1.69174e9	+	9.76728e8i	0.976817	+	0.563966i
$205$	−7.42714e8	+	4.28806e8i	−0.420539	+	0.242798i
$206$	−2.97151e8	+	5.14680e8i	−0.165009	+	0.285804i
$207$	6.30924e8	−	1.09279e9i	0.343633	−	0.595190i
$208$		−	2.93210e8i		−	0.156648i
$209$	9.16027e8	−	3.78155e8i	0.480091	−	0.198191i
$210$	3.52089e8			0.181040
$211$	−2.70804e8	−	1.56349e8i	−0.136623	−	0.0788796i	0.430130	−	0.902767i	$-0.358468\pi$
$211$	−2.70804e8	−	1.56349e8i	−0.136623	−	0.0788796i	−0.566754	+	0.823887i	$0.691801\pi$
$212$	1.21704e9	+	7.02658e8i	0.602505	+	0.347857i
$213$	3.78474e8	+	6.55536e8i	0.183873	+	0.318477i
$214$	−2.14859e8	+	3.72146e8i	−0.102447	+	0.177443i
$215$	−5.02433e8	−	8.70239e8i	−0.235139	−	0.407272i
$216$	3.86264e8			0.177447
$217$			7.99571e7i			0.0360594i
$218$	1.19038e9	+	2.06180e9i	0.527060	+	0.912894i
$219$	−5.84223e9	+	3.37302e9i	−2.53982	+	1.46636i
$220$	−6.48524e8			−0.276844
$221$		−	2.20950e9i		−	0.926243i
$222$	3.68969e9	−	2.13024e9i	1.51907	−	0.877036i
$223$	−2.18744e9	−	1.26292e9i	−0.884537	−	0.510687i	−0.0123850	−	0.999923i	$-0.503942\pi$
$223$	−2.18744e9	−	1.26292e9i	−0.884537	−	0.510687i	−0.872151	+	0.489236i	$0.837276\pi$
$224$	6.06587e7	−	3.50213e7i	0.0240936	−	0.0139104i
$225$	2.32322e8	−	4.02393e8i	0.0906483	−	0.157007i
$226$	−2.65225e8	+	4.59384e8i	−0.101667	+	0.176093i
$227$			6.79047e8i			0.255739i	0.991791	+	0.127869i	$0.0408138\pi$
$227$			6.79047e8i			0.255739i	−0.991791	+	0.127869i	$0.959186\pi$
$228$	7.86817e8	+	1.90595e9i	0.291162	+	0.705298i
$229$	−3.81413e9			−1.38693			−0.693463	−	0.720492i	$-0.743916\pi$
$229$	−3.81413e9			−1.38693			−0.693463	+	0.720492i	$0.743916\pi$
$230$	−9.44793e8	−	5.45477e8i	−0.337618	−	0.194924i
$231$	−3.07604e8	−	1.77595e8i	−0.108030	−	0.0623711i
$232$	1.10305e8	+	1.91055e8i	0.0380755	+	0.0659486i
$233$	−2.73601e9	+	4.73892e9i	−0.928314	+	1.60789i	−0.142170	+	0.989842i	$0.545408\pi$
$233$	−2.73601e9	+	4.73892e9i	−0.928314	+	1.60789i	−0.786144	+	0.618044i	$0.787925\pi$
$234$	−8.82655e8	−	1.52880e9i	−0.294393	−	0.509904i
$235$	−3.76244e9			−1.23367
$236$		−	1.23544e9i		−	0.398266i
$237$	3.93204e9	+	6.81050e9i	1.24631	+	2.15867i
$238$	4.57097e8	−	2.63905e8i	0.142462	−	0.0822507i
$239$	1.01562e9			0.311270			0.155635	−	0.987815i	$-0.450258\pi$
$239$	1.01562e9			0.311270			0.155635	+	0.987815i	$0.450258\pi$
$240$		−	1.34937e9i		−	0.406710i
$241$	−5.27900e9	+	3.04783e9i	−1.56489	+	0.903489i	−0.568138	+	0.822933i	$0.692336\pi$
$241$	−5.27900e9	+	3.04783e9i	−1.56489	+	0.903489i	−0.996750	+	0.0805559i	$0.974330\pi$
$242$	−1.53369e9	−	8.85478e8i	−0.447175	−	0.258176i
$243$	−4.10974e9	+	2.37276e9i	−1.17866	+	0.680501i
$244$	−8.98696e8	+	1.55659e9i	−0.253544	+	0.439152i
$245$	−1.87289e9	+	3.24395e9i	−0.519815	+	0.900346i
$246$			1.80013e9i			0.491545i
$247$	1.42198e9	−	1.84860e9i	0.382037	−	0.496656i
$248$	3.06432e8			0.0810080
$249$	1.34398e9	+	7.75949e8i	0.349620	+	0.201853i
$250$	2.20214e9	+	1.27141e9i	0.563748	+	0.325480i
$251$	1.15084e9	+	1.99331e9i	0.289948	+	0.502205i	0.973797	−	0.227419i	$-0.0730286\pi$
$251$	1.15084e9	+	1.99331e9i	0.289948	+	0.502205i	−0.683849	+	0.729624i	$0.739695\pi$
$252$	2.10850e8	−	3.65203e8i	0.0522844	−	0.0905592i
$253$	5.50282e8	+	9.53116e8i	0.134308	+	0.232629i
$254$	2.98899e9			0.718107
$255$		−	1.01682e10i		−	2.40483i
$256$	−1.34218e8	−	2.32472e8i	−0.0312500	−	0.0541266i
$257$	9.31807e8	−	5.37979e8i	0.213596	−	0.123320i	−0.389385	−	0.921075i	$-0.627313\pi$
$257$	9.31807e8	−	5.37979e8i	0.213596	−	0.123320i	0.602982	+	0.797755i	$0.293979\pi$
$258$	−2.10921e9			−0.476038
$259$		−	1.15115e9i		−	0.255820i
$260$	−1.32176e9	+	7.63116e8i	−0.289240	+	0.166993i
$261$	1.15027e9	+	6.64108e8i	0.247878	+	0.143112i
$262$	−7.01655e7	+	4.05101e7i	−0.0148908	+	0.00859722i
$263$	2.98341e9	−	5.16742e9i	0.623577	−	1.08007i	−0.365237	−	0.930914i	$-0.619012\pi$
$263$	2.98341e9	−	5.16742e9i	0.623577	−	1.08007i	0.988814	−	0.149152i	$-0.0476545\pi$
$264$	−6.80626e8	+	1.17888e9i	−0.140118	+	0.242691i
$265$		−	7.31501e9i		−	1.48331i
$266$	5.52277e8	+	7.33770e7i	0.110314	+	0.0146566i
$267$	1.19841e10			2.35810
$268$	−3.81787e9	−	2.20425e9i	−0.740085	−	0.427288i
$269$	8.38245e8	+	4.83961e8i	0.160089	+	0.0924275i	0.577904	−	0.816105i	$-0.303871\pi$
$269$	8.38245e8	+	4.83961e8i	0.160089	+	0.0924275i	−0.417815	+	0.908532i	$0.637204\pi$
$270$	−1.00530e9	−	1.74123e9i	−0.189165	−	0.327643i
$271$	2.39057e9	−	4.14058e9i	0.443224	−	0.767687i	−0.554702	−	0.832049i	$-0.687168\pi$
$271$	2.39057e9	−	4.14058e9i	0.443224	−	0.767687i	0.997927	+	0.0643617i	$0.0205011\pi$
$272$	−1.01140e9	−	1.75180e9i	−0.184777	−	0.320044i
$273$	−8.35903e8			−0.150489
$274$			2.16953e9i			0.384914i
$275$	2.02627e8	+	3.50961e8i	0.0354297	+	0.0613660i
$276$	−1.98312e9	+	1.14496e9i	−0.341754	+	0.197312i
$277$	−1.04586e9			−0.177646			−0.0888231	−	0.996047i	$-0.528311\pi$
$277$	−1.04586e9			−0.177646			−0.0888231	+	0.996047i	$0.528311\pi$
$278$		−	4.13144e9i		−	0.691707i
$279$	1.59774e9	−	9.22457e8i	0.263688	−	0.152240i
$280$	−3.15743e8	−	1.82294e8i	−0.0513691	−	0.0296580i
$281$	3.48382e9	−	2.01138e9i	0.558766	−	0.322604i	−0.193884	−	0.981024i	$-0.562109\pi$
$281$	3.48382e9	−	2.01138e9i	0.558766	−	0.322604i	0.752650	+	0.658421i	$0.228775\pi$
$282$	−3.94868e9	+	6.83932e9i	−0.624390	+	1.08147i
$283$	−4.78843e9	+	8.29380e9i	−0.746530	+	1.29303i	0.202947	+	0.979190i	$0.434948\pi$
$283$	−4.78843e9	+	8.29380e9i	−0.746530	+	1.29303i	−0.949477	+	0.313837i	$0.898385\pi$
$284$		−	7.83821e8i		−	0.120488i
$285$	6.54400e9	−	8.50734e9i	0.991891	−	1.28948i
$286$	1.53968e9			0.230126
$287$	4.21220e8	+	2.43191e8i	0.0620842	+	0.0358443i
$288$	−1.39963e9	−	8.08075e8i	−0.203443	−	0.117458i
$289$	−4.13360e9	−	7.15961e9i	−0.592567	−	1.02636i
$290$	5.74167e8	−	9.94486e8i	0.0811795	−	0.140607i
$291$	4.58017e9	+	7.93308e9i	0.638718	+	1.10629i
$292$	6.98553e9			0.960878
$293$		−	1.95159e9i		−	0.264801i	−0.991196	−	0.132400i	$-0.957732\pi$
$293$		−	1.95159e9i		−	0.264801i	0.991196	−	0.132400i	$-0.0422684\pi$
$294$	3.93121e9	+	6.80905e9i	0.526183	+	0.911375i
$295$	−5.56920e9	+	3.21538e9i	−0.735368	+	0.424565i
$296$	−4.41175e9			−0.574703
$297$			2.02831e9i			0.260681i
$298$	2.42261e9	−	1.39869e9i	0.307198	−	0.177361i
$299$	2.24306e9	+	1.29503e9i	0.280644	+	0.162030i
$300$	−7.30235e8	+	4.21601e8i	−0.0901524	+	0.0520495i
$301$	−2.84947e8	+	4.93543e8i	−0.0347135	+	0.0601256i
$302$	−2.65538e9	+	4.59925e9i	−0.319226	+	0.552916i
$303$			1.55342e10i			1.84297i
$304$	2.81214e8	−	2.11658e9i	0.0329263	−	0.247822i
$305$	9.35587e9			1.08115
$306$	−1.05469e10	−	6.08928e9i	−1.20293	−	0.694513i
$307$	1.36112e10	+	7.85845e9i	1.53230	+	0.884674i	0.999255	+	0.0385877i	$0.0122859\pi$
$307$	1.36112e10	+	7.85845e9i	1.53230	+	0.884674i	0.533046	+	0.846087i	$0.321047\pi$
$308$	1.83900e8	+	3.18525e8i	0.0204352	+	0.0353949i
$309$	3.24661e9	−	5.62330e9i	0.356120	−	0.616818i
$310$	−7.97527e8	−	1.38136e9i	−0.0863572	−	0.149575i
$311$	5.54639e9			0.592883			0.296441	−	0.955051i	$-0.404200\pi$
$311$	5.54639e9			0.592883			0.296441	+	0.955051i	$0.404200\pi$
$312$			3.20356e9i			0.338076i
$313$	−3.64650e9	−	6.31591e9i	−0.379925	−	0.658050i	0.611126	−	0.791534i	$-0.290717\pi$
$313$	−3.64650e9	−	6.31591e9i	−0.379925	−	0.658050i	−0.991051	+	0.133484i	$0.957384\pi$
$314$	6.72026e9	−	3.87994e9i	0.691302	−	0.399123i
$315$	−2.19505e9			−0.222948
$316$		−	8.14328e9i		−	0.816679i
$317$	−1.02368e10	+	5.91024e9i	−1.01374	+	0.585286i	−0.912286	−	0.409554i	$-0.865684\pi$
$317$	−1.02368e10	+	5.91024e9i	−1.01374	+	0.585286i	−0.101459	+	0.994840i	$0.532351\pi$
$318$	−1.32971e10	−	7.67711e9i	−1.30032	−	0.750739i
$319$	−1.00325e9	+	5.79225e8i	−0.0968825	+	0.0559351i
$320$	−6.98636e8	+	1.21007e9i	−0.0666271	+	0.115402i
$321$	2.34750e9	−	4.06600e9i	0.221099	−	0.382954i
$322$			6.18718e8i			0.0575532i
$323$	2.11910e9	−	1.59496e10i	0.194689	−	1.46534i
$324$	3.10187e9			0.281477
$325$	8.25949e8	+	4.76862e8i	0.0740320	+	0.0427424i
$326$	6.55584e9	+	3.78502e9i	0.580441	+	0.335118i
$327$	−1.30059e10	−	2.25268e10i	−1.13749	−	1.97019i
$328$	9.32020e8	−	1.61431e9i	0.0805248	−	0.139473i
$329$	1.06691e9	+	1.84794e9i	0.0910631	+	0.157726i
$330$	7.08565e9			0.597481
$331$		−	3.77809e9i		−	0.314746i	−0.987539	−	0.157373i	$-0.949698\pi$
$331$		−	3.77809e9i		−	0.314746i	0.987539	−	0.157373i	$-0.0503025\pi$
$332$	−8.03497e8	−	1.39170e9i	−0.0661351	−	0.114549i
$333$	−2.30029e10	+	1.32807e10i	−1.87071	+	1.08005i
$334$	7.47677e9			0.600797
$335$			2.29473e10i			1.82201i
$336$	−6.62746e8	+	3.82636e8i	−0.0519984	+	0.0300213i
$337$	−1.52788e9	−	8.82120e8i	−0.118459	−	0.0683924i	0.439600	−	0.898194i	$-0.355120\pi$
$337$	−1.52788e9	−	8.82120e8i	−0.118459	−	0.0683924i	−0.558059	+	0.829801i	$0.688454\pi$
$338$	−4.85448e9	+	2.80274e9i	−0.371943	+	0.214741i
$339$	2.89780e9	−	5.01914e9i	0.219417	−	0.380041i
$340$	−5.26460e9	+	9.11856e9i	−0.393958	+	0.682355i
$341$			1.60911e9i			0.119006i
$342$	−4.90531e9	−	1.18824e10i	−0.358560	−	0.868561i
$343$	4.30269e9			0.310859
$344$	1.89148e9	+	1.09205e9i	0.135073	+	0.0779845i
$345$	1.03226e10	+	5.95978e9i	0.728642	+	0.420682i
$346$	5.54914e9	+	9.61139e9i	0.387187	+	0.670628i
$347$	−1.19736e10	+	2.07388e10i	−0.825858	+	1.43043i	0.0754042	+	0.997153i	$0.475975\pi$
$347$	−1.19736e10	+	2.07388e10i	−0.825858	+	1.43043i	−0.901262	+	0.433275i	$0.857358\pi$
$348$	−1.20518e9	−	2.08743e9i	−0.0821739	−	0.142329i
$349$	−4.67026e9			−0.314803			−0.157402	−	0.987535i	$-0.550312\pi$
$349$	−4.67026e9			−0.314803			−0.157402	+	0.987535i	$0.550312\pi$
$350$			2.27827e8i			0.0151822i
$351$	2.38671e9	+	4.13389e9i	0.157243	+	0.272352i
$352$	1.22073e9	−	7.04790e8i	0.0795152	−	0.0459081i
$353$	−7.11757e9			−0.458387			−0.229194	−	0.973381i	$-0.573609\pi$
$353$	−7.11757e9			−0.458387			−0.229194	+	0.973381i	$0.573609\pi$
$354$			1.34982e10i			0.859532i
$355$	−3.53336e9	+	2.03999e9i	−0.222472	+	0.128444i
$356$	−1.07470e10	−	6.20481e9i	−0.669097	−	0.386303i
$357$	−4.99415e9	+	2.88337e9i	−0.307460	+	0.177512i
$358$	−9.73317e9	+	1.68583e10i	−0.592546	+	1.02632i
$359$	2.89227e9	−	5.00955e9i	0.174125	−	0.301593i	−0.765733	−	0.643158i	$-0.777624\pi$
$359$	2.89227e9	−	5.00955e9i	0.174125	−	0.301593i	0.939858	+	0.341565i	$0.110957\pi$
$360$			8.41245e9i			0.500856i
$361$	1.20377e10	−	1.19806e10i	0.708787	−	0.705423i
$362$	−8.61437e9			−0.501637
$363$	1.67569e10	+	9.67457e9i	0.965086	+	0.557193i
$364$	7.49614e8	+	4.32790e8i	0.0427004	+	0.0246531i
$365$	−1.81807e10	−	3.14899e10i	−1.02433	−	1.77419i
$366$	9.81899e9	−	1.70070e10i	0.547195	−	0.947770i
$367$	−2.18913e9	−	3.79169e9i	−0.120672	−	0.209011i	0.799361	−	0.600852i	$-0.205172\pi$
$367$	−2.18913e9	−	3.79169e9i	−0.120672	−	0.209011i	−0.920033	+	0.391841i	$0.871838\pi$
$368$	2.37121e9			0.129294
$369$		−	1.12227e10i		−	0.605329i
$370$	1.14821e10	+	1.98876e10i	0.612653	+	1.06115i
$371$	−3.59279e9	+	2.07430e9i	−0.189643	+	0.109490i
$372$	−3.34802e9			−0.174830
$373$			9.54874e9i			0.493299i	0.969105	+	0.246650i	$0.0793297\pi$
$373$			9.54874e9i			0.493299i	−0.969105	+	0.246650i	$0.920670\pi$
$374$	9.19889e9	−	5.31098e9i	0.470164	−	0.271449i
$375$	−2.40602e10	−	1.38912e10i	−1.21667	−	0.702447i
$376$	7.08213e9	−	4.08887e9i	0.354334	−	0.204575i
$377$	−1.36314e9	+	2.36103e9i	−0.0674802	+	0.116879i
$378$	−5.70141e8	+	9.87512e8i	−0.0279264	+	0.0483699i
$379$		−	1.13989e9i		−	0.0552467i	−0.999618	−	0.0276233i	$-0.991206\pi$
$379$		−	1.13989e9i		−	0.0552467i	0.999618	−	0.0276233i	$-0.00879390\pi$
$380$	−1.02732e10	+	4.24098e9i	−0.492686	+	0.203391i
$381$	−3.26571e10			−1.54981
$382$	−7.58303e9	−	4.37806e9i	−0.356114	−	0.205603i
$383$	2.24068e10	+	1.29365e10i	1.04132	+	0.601206i	0.920207	−	0.391433i	$-0.128020\pi$
$383$	2.24068e10	+	1.29365e10i	1.04132	+	0.601206i	0.121113	+	0.992639i	$0.461354\pi$
$384$	1.46644e9	+	2.53994e9i	0.0674433	+	0.116815i
$385$	9.57246e8	−	1.65800e9i	0.0435693	−	0.0754643i
$386$	−7.49997e9	−	1.29903e10i	−0.337839	−	0.585155i
$387$	1.31496e10			0.586232
$388$		−	9.48555e9i		−	0.418539i
$389$	1.50156e10	+	2.60078e10i	0.655759	+	1.13581i	0.981703	+	0.190419i	$0.0609847\pi$
$389$	1.50156e10	+	2.60078e10i	0.655759	+	1.13581i	−0.325944	+	0.945389i	$0.605682\pi$
$390$	1.44413e10	−	8.33766e9i	0.624233	−	0.360401i
$391$	1.78684e10			0.764501
$392$		−	8.14155e9i		−	0.344797i
$393$	7.66615e8	−	4.42606e8i	0.0321371	−	0.0185544i
$394$	1.66804e10	+	9.63043e9i	0.692184	+	0.399633i
$395$	−3.67089e10	+	2.11939e10i	−1.50794	+	0.870607i
$396$	4.24328e9	−	7.34958e9i	0.172552	−	0.298869i
$397$	1.75238e10	−	3.03521e10i	0.705451	−	1.22188i	−0.261078	−	0.965318i	$-0.584078\pi$
$397$	1.75238e10	−	3.03521e10i	0.705451	−	1.22188i	0.966529	−	0.256559i	$-0.0825887\pi$
$398$		−	3.35414e10i		−	1.33675i
$399$	−6.03408e9	−	8.01704e8i	−0.238078	−	0.0316317i
$400$	8.73138e8			0.0341070
$401$	2.79554e10	+	1.61401e10i	1.08116	+	0.624207i	0.931208	−	0.364487i	$-0.118756\pi$
$401$	2.79554e10	+	1.61401e10i	1.08116	+	0.624207i	0.149949	+	0.988694i	$0.452089\pi$
$402$	4.17133e10	+	2.40832e10i	1.59724	+	0.922167i
$403$	1.89343e9	+	3.27951e9i	0.0717842	+	0.124334i
$404$	8.04287e9	−	1.39307e10i	0.301916	−	0.522933i
$405$	−8.07298e9	−	1.39828e10i	−0.300064	−	0.519726i
$406$	−6.51261e8			−0.0239690
$407$		−	2.31665e10i		−	0.844273i
$408$	1.10504e10	+	1.91399e10i	0.398784	+	0.690714i
$409$	−1.41907e9	+	8.19303e8i	−0.0507121	+	0.0292787i	−0.525142	−	0.851015i	$-0.675988\pi$
$409$	−1.41907e9	+	8.19303e8i	−0.0507121	+	0.0292787i	0.474430	+	0.880293i	$0.342654\pi$
$410$	−9.70278e9			−0.343369
$411$		−	2.37039e10i		−	0.830717i
$412$	−5.82294e9	+	3.36188e9i	−0.202094	+	0.116679i
$413$	3.15849e9	+	1.82355e9i	0.108562	+	0.0626785i
$414$	1.23635e10	−	7.13809e9i	0.420863	−	0.242986i
$415$	−4.18240e9	+	7.24412e9i	−0.141004	+	0.244227i
$416$	1.65865e9	−	2.87286e9i	0.0553836	−	0.0959272i
$417$			4.51393e10i			1.49283i
$418$	1.11144e10	+	1.47668e9i	0.364066	+	0.0483707i
$419$	−3.26473e10			−1.05923			−0.529615	−	0.848238i	$-0.677664\pi$
$419$	−3.26473e10			−1.05923			−0.529615	+	0.848238i	$0.677664\pi$
$420$	3.44975e9	+	1.99172e9i	0.110864	+	0.0640074i
$421$	−9.21424e9	−	5.31985e9i	−0.293313	−	0.169344i	0.346122	−	0.938190i	$-0.387498\pi$
$421$	−9.21424e9	−	5.31985e9i	−0.293313	−	0.169344i	−0.639435	+	0.768845i	$0.720832\pi$
$422$	−1.76888e9	−	3.06380e9i	−0.0557763	−	0.0966074i
$423$	2.46176e10	−	4.26389e10i	0.768924	−	1.33182i
$424$	7.94966e9	+	1.37692e10i	0.245972	+	0.426036i
$425$	6.57957e9			0.201670
$426$			8.56388e9i			0.260035i
$427$	−2.65302e9	−	4.59517e9i	−0.0798048	−	0.138226i
$428$	−4.21035e9	+	2.43085e9i	−0.125471	+	0.0724407i
$429$	−1.68222e10			−0.496654
$430$		−	1.13688e10i		−	0.332536i
$431$	−4.29722e10	+	2.48100e10i	−1.24531	+	0.718982i	−0.970171	−	0.242422i	$-0.922058\pi$
$431$	−4.29722e10	+	2.48100e10i	−1.24531	+	0.718982i	−0.275142	+	0.961404i	$0.588725\pi$
$432$	3.78460e9	+	2.18504e9i	0.108664	+	0.0627371i
$433$	3.55575e10	−	2.05291e10i	1.01153	−	0.584008i	0.0998913	−	0.994998i	$-0.468151\pi$
$433$	3.55575e10	−	2.05291e10i	1.01153	−	0.584008i	0.911639	+	0.410991i	$0.134817\pi$
$434$	−4.52306e8	+	7.83417e8i	−0.0127489	+	0.0220818i
$435$	−6.27324e9	+	1.08656e10i	−0.175200	+	0.303456i
$436$			2.69352e10i			0.745375i
$437$	1.49498e10	+	1.14996e10i	0.409929	+	0.315325i
$438$	−7.63226e10			−2.07375
$439$	5.47784e10	+	3.16263e10i	1.47486	+	0.851512i	0.999599	−	0.0283320i	$-0.00901958\pi$
$439$	5.47784e10	+	3.16263e10i	1.47486	+	0.851512i	0.475263	+	0.879844i	$0.342353\pi$
$440$	−6.35421e9	−	3.66861e9i	−0.169532	−	0.0978792i
$441$	−2.45086e10	−	4.24502e10i	−0.647984	−	1.12234i
$442$	1.24988e10	−	2.16486e10i	0.327476	−	0.567206i
$443$	2.86968e9	+	4.97043e9i	0.0745106	+	0.129056i	0.900873	−	0.434082i	$-0.142927\pi$
$443$	2.86968e9	+	4.97043e9i	0.0745106	+	0.129056i	−0.826363	+	0.563138i	$0.809594\pi$
$444$	4.82019e10			1.24032
$445$			6.45951e10i			1.64725i
$446$	−1.42883e10	−	2.47480e10i	−0.361111	−	0.625462i
$447$	−2.64690e10	+	1.52819e10i	−0.662990	+	0.382777i
$448$	7.92442e8			0.0196723
$449$		−	7.78763e10i		−	1.91611i	−0.286589	−	0.958054i	$-0.592521\pi$
$449$		−	7.78763e10i		−	1.91611i	0.286589	−	0.958054i	$-0.407479\pi$
$450$	4.55256e9	−	2.62842e9i	0.111021	−	0.0640980i
$451$	8.47688e9	+	4.89413e9i	0.204894	+	0.118296i
$452$	−5.19733e9	+	3.00068e9i	−0.124516	+	0.0718896i
$453$	2.90122e10	−	5.02506e10i	0.688950	−	1.19330i
$454$	−3.84127e9	+	6.65328e9i	−0.0904173	+	0.156607i
$455$		−	4.50555e9i		−	0.105124i
$456$	−3.07250e9	+	2.31254e10i	−0.0710611	+	0.534846i
$457$	−7.37734e10			−1.69136			−0.845678	−	0.533694i	$-0.820803\pi$
$457$	−7.37734e10			−1.69136			−0.845678	+	0.533694i	$0.820803\pi$
$458$	−3.73707e10	−	2.15760e10i	−0.849316	−	0.490353i
$459$	2.85190e10	+	1.64655e10i	0.642516	+	0.370957i
$460$	−6.17136e9	−	1.06891e10i	−0.137832	−	0.238732i
$461$	3.84745e10	−	6.66398e10i	0.851862	−	1.47547i	−0.0276647	−	0.999617i	$-0.508807\pi$
$461$	3.84745e10	−	6.66398e10i	0.851862	−	1.47547i	0.879526	−	0.475850i	$-0.157860\pi$
$462$	−2.00926e9	−	3.48014e9i	−0.0441030	−	0.0763887i
$463$	7.18848e10			1.56428			0.782138	−	0.623106i	$-0.214129\pi$
$463$	7.18848e10			1.56428			0.782138	+	0.623106i	$0.214129\pi$
$464$			2.49593e9i			0.0538468i
$465$	8.71363e9	+	1.50925e10i	0.186375	+	0.322811i
$466$	−5.36147e10	+	3.09545e10i	−1.13695	+	0.656417i
$467$	1.19258e10			0.250738			0.125369	−	0.992110i	$-0.459989\pi$
$467$	1.19258e10			0.250738			0.125369	+	0.992110i	$0.459989\pi$
$468$		−	1.99722e10i		−	0.416335i
$469$	1.12706e10	−	6.50710e9i	0.232947	−	0.134492i
$470$	−3.68642e10	−	2.12836e10i	−0.755464	−	0.436167i
$471$	−7.34243e10	+	4.23916e10i	−1.49196	+	0.861382i
$472$	6.98870e9	−	1.21048e10i	0.140808	−	0.243887i
$473$	−5.73445e9	+	9.93236e9i	−0.114564	+	0.198430i
$474$			8.89720e10i			1.76254i
$475$	5.50487e9	+	4.23445e9i	0.108137	+	0.0831807i
$476$	5.97148e9			0.116320
$477$	8.28993e10	+	4.78619e10i	1.60132	+	0.924521i
$478$	9.95096e9	+	5.74519e9i	0.190613	+	0.110051i
$479$	4.89947e10	+	8.48614e10i	0.930695	+	1.61201i	0.782136	+	0.623108i	$0.214130\pi$
$479$	4.89947e10	+	8.48614e10i	0.930695	+	1.61201i	0.148559	+	0.988904i	$0.452536\pi$
$480$	7.63317e9	−	1.32210e10i	0.143794	−	0.249058i
$481$	−2.72600e10	−	4.72156e10i	−0.509266	−	0.882075i
$482$	−6.89646e10			−1.27773
$483$		−	6.76000e9i		−	0.124210i
$484$	−1.00180e10	−	1.73518e10i	−0.182558	−	0.316200i
$485$	−4.27596e10	+	2.46873e10i	−0.772800	+	0.446176i
$486$	−5.36895e10			−0.962374
$487$			8.39330e10i			1.49217i	0.665853	+	0.746083i	$0.268068\pi$
$487$			8.39330e10i			1.49217i	−0.665853	+	0.746083i	$0.731932\pi$
$488$	−1.76108e10	+	1.01676e10i	−0.310527	+	0.179283i
$489$	−7.16279e10	−	4.13544e10i	−1.25270	−	0.723247i
$490$	−3.67011e10	+	2.11894e10i	−0.636641	+	0.367565i
$491$	1.41607e10	−	2.45270e10i	0.243646	−	0.422007i	−0.718104	−	0.695935i	$-0.754990\pi$
$491$	1.41607e10	−	2.45270e10i	0.243646	−	0.422007i	0.961750	+	0.273929i	$0.0883233\pi$
$492$	−1.01831e10	+	1.76376e10i	−0.173788	+	0.301009i
$493$			1.88082e10i			0.318390i
$494$	2.43898e10	−	1.00686e10i	0.409543	−	0.169068i
$495$	−4.41746e10			−0.735786
$496$	3.00241e9	+	1.73344e9i	0.0496070	+	0.0286406i
$497$	2.00390e9	+	1.15695e9i	0.0328435	+	0.0189622i
$498$	8.77886e9	+	1.52054e10i	0.142732	+	0.247219i
$499$	5.41163e10	−	9.37322e10i	0.872823	−	1.51177i	0.0137587	−	0.999905i	$-0.495620\pi$
$499$	5.41163e10	−	9.37322e10i	0.872823	−	1.51177i	0.859064	−	0.511868i	$-0.171046\pi$
$500$	1.43843e10	+	2.49144e10i	0.230149	+	0.398630i
$501$	−8.16898e10			−1.29663
$502$			2.60406e10i			0.410049i
$503$	3.81949e10	+	6.61554e10i	0.596668	+	1.03346i	0.993309	+	0.115486i	$0.0368425\pi$
$503$	3.81949e10	+	6.61554e10i	0.596668	+	1.03346i	−0.396641	+	0.917974i	$0.629824\pi$
$504$	4.13180e9	−	2.38550e9i	0.0640350	−	0.0369706i
$505$	−8.37302e10			−1.28741
$506$			1.24515e10i			0.189941i
$507$	5.30392e10	−	3.06222e10i	0.802722	−	0.463452i
$508$	2.92860e10	+	1.69083e10i	0.439749	+	0.253889i
$509$	−4.16982e10	+	2.40745e10i	−0.621221	+	0.358662i	−0.777344	−	0.629075i	$-0.783434\pi$
$509$	−4.16982e10	+	2.40745e10i	−0.621221	+	0.358662i	0.156123	+	0.987738i	$0.450100\pi$
$510$	5.75201e10	−	9.96277e10i	0.850234	−	1.47265i
$511$	−1.03109e10	+	1.78590e10i	−0.151222	+	0.261923i
$512$		−	3.03700e9i		−	0.0441942i
$513$	1.32640e10	+	3.21301e10i	0.191516	+	0.463920i
$514$	1.21731e10			0.174401
$515$	3.03098e10	+	1.74994e10i	0.430878	+	0.248768i
$516$	−2.06660e10	−	1.19315e10i	−0.291513	−	0.168305i
$517$	2.14711e10	+	3.71890e10i	0.300532	+	0.520537i
$518$	6.51191e9	−	1.12790e10i	0.0904460	−	0.156657i
$519$	−6.06289e10	−	1.05012e11i	−0.835622	−	1.44734i
$520$	−1.72673e10			−0.236163
$521$			9.88180e10i			1.34117i	0.741831	+	0.670587i	$0.233958\pi$
$521$			9.88180e10i			1.34117i	−0.741831	+	0.670587i	$0.766042\pi$
$522$	7.51353e9	+	1.30138e10i	0.101196	+	0.175276i
$523$	−2.51149e10	+	1.45001e10i	−0.335680	+	0.193805i	−0.658360	−	0.752703i	$-0.728750\pi$
$523$	−2.51149e10	+	1.45001e10i	−0.335680	+	0.193805i	0.322680	+	0.946508i	$0.395416\pi$
$524$	−9.16638e8			−0.0121583
$525$		−	2.48920e9i		−	0.0327659i
$526$	5.84627e10	−	3.37534e10i	0.763723	−	0.440935i
$527$	2.26248e10	+	1.30624e10i	0.293320	+	0.169349i
$528$	−1.33375e10	+	7.70041e9i	−0.171608	+	0.0990782i
$529$	2.86825e10	−	4.96796e10i	0.366264	−	0.634388i
$530$	4.13799e10	−	7.16721e10i	0.524428	−	0.908337i
$531$		−	8.41526e10i		−	1.05850i
$532$	4.99611e9	+	3.84310e9i	0.0623714	+	0.0479772i
$533$	2.30356e10			0.285424
$534$	1.17420e11	+	6.77926e10i	1.44403	+	0.833714i
$535$	2.19159e10	+	1.26531e10i	0.267512	+	0.154448i
$536$	−2.49382e10	−	4.31942e10i	−0.302138	−	0.523319i
$537$	1.06343e11	−	1.84191e11i	1.27882	−	2.21499i
$538$	5.47539e9	+	9.48366e9i	0.0653561	+	0.113200i
$539$	4.27521e10			0.506527
$540$		−	2.27473e10i		−	0.267519i
$541$	−1.36497e10	−	2.36420e10i	−0.159343	−	0.275991i	0.775289	−	0.631607i	$-0.217604\pi$
$541$	−1.36497e10	−	2.36420e10i	−0.159343	−	0.275991i	−0.934632	+	0.355616i	$0.884271\pi$
$542$	4.68454e10	−	2.70462e10i	0.542837	−	0.313407i
$543$	9.41190e10			1.08263
$544$		−	2.28855e10i		−	0.261315i
$545$	1.21421e11	−	7.01022e10i	1.37628	−	0.794595i
$546$	−8.19014e9	−	4.72858e9i	−0.0921554	−	0.0532060i
$547$	−1.00866e10	+	5.82348e9i	−0.112666	+	0.0650479i	−0.555274	−	0.831667i	$-0.687387\pi$
$547$	−1.00866e10	+	5.82348e9i	−0.112666	+	0.0650479i	0.442608	+	0.896715i	$0.354053\pi$
$548$	−1.22727e10	+	2.12570e10i	−0.136088	+	0.235711i
$549$	−6.12152e10	+	1.06028e11i	−0.673861	+	1.16716i
$550$			4.58493e9i			0.0501052i
$551$	−1.21045e10	+	1.57361e10i	−0.131323	+	0.170722i
$552$	−2.59074e10			−0.279041
$553$	2.08189e10	+	1.20198e10i	0.222617	+	0.128528i
$554$	−1.02473e10	−	5.91630e9i	−0.108786	−	0.0628074i
$555$	−1.25451e11	−	2.17288e11i	−1.32222	−	2.29015i
$556$	2.33709e10	−	4.04797e10i	0.244555	−	0.423582i
$557$	3.64050e8	+	6.30554e8i	0.00378217	+	0.00655090i	0.867910	−	0.496721i	$-0.165463\pi$
$557$	3.64050e8	+	6.30554e8i	0.00378217	+	0.00655090i	−0.864128	+	0.503272i	$0.832129\pi$
$558$	2.08728e10			0.215300
$559$			2.69908e10i			0.276420i
$560$	−2.06243e9	−	3.57223e9i	−0.0209714	−	0.0363234i
$561$	−1.00505e11	+	5.80268e10i	−1.01470	+	0.585837i
$562$	4.55124e10			0.456231
$563$			1.27074e10i			0.126480i	0.997998	+	0.0632402i	$0.0201434\pi$
$563$			1.27074e10i			0.126480i	−0.997998	+	0.0632402i	$0.979857\pi$
$564$	−7.73781e10	+	4.46742e10i	−0.764718	+	0.441510i
$565$	2.70534e10	+	1.56193e10i	0.265477	+	0.153273i
$566$	−9.38336e10	+	5.41749e10i	−0.914308	+	0.527876i
$567$	−4.57847e9	+	7.93015e9i	−0.0442985	+	0.0767272i
$568$	4.43396e9	−	7.67985e9i	0.0425989	−	0.0737835i
$569$		−	3.11677e10i		−	0.297342i	−0.988887	−	0.148671i	$-0.952501\pi$
$569$		−	3.11677e10i		−	0.297342i	0.988887	−	0.148671i	$-0.0474995\pi$
$570$	1.12243e11	−	4.63361e10i	1.06331	−	0.438955i
$571$	−4.77705e10			−0.449382			−0.224691	−	0.974430i	$-0.572137\pi$
$571$	−4.77705e10			−0.449382			−0.224691	+	0.974430i	$0.572137\pi$
$572$	1.50857e10	+	8.70973e9i	0.140923	+	0.0813618i
$573$	8.28507e10	+	4.78339e10i	0.768560	+	0.443728i
$574$	2.75139e9	+	4.76556e9i	0.0253458	+	0.0439001i
$575$	−3.85641e9	+	6.67950e9i	−0.0352786	+	0.0611044i
$576$	−9.14232e9	−	1.58350e10i	−0.0830551	−	0.143856i
$577$	5.37829e10			0.485222			0.242611	−	0.970124i	$-0.421996\pi$
$577$	5.37829e10			0.485222			0.242611	+	0.970124i	$0.421996\pi$
$578$		−	9.35327e10i		−	0.838016i
$579$	8.19433e10	+	1.41930e11i	0.729120	+	1.26287i
$580$	1.12513e10	−	6.49596e9i	0.0994241	−	0.0574025i
$581$	4.74397e9			0.0416330
$582$			1.03637e11i			0.903284i
$583$	−7.23035e10	+	4.17445e10i	−0.625872	+	0.361347i
$584$	6.84440e10	+	3.95161e10i	0.588415	+	0.339722i
$585$	−9.00321e10	+	5.19801e10i	−0.768731	+	0.443827i
$586$	1.10399e10	−	1.91216e10i	0.0936212	−	0.162157i
$587$	6.54532e10	−	1.13368e11i	0.551288	−	0.954858i	−0.446894	−	0.894587i	$-0.647470\pi$
$587$	6.54532e10	−	1.13368e11i	0.551288	−	0.954858i	0.998182	−	0.0602717i	$-0.0191967\pi$
$588$			8.89531e10i			0.744135i
$589$	1.05226e10	+	2.54896e10i	0.0874306	+	0.211788i
$590$	−7.27557e10			−0.600425
$591$	−1.82247e11	−	1.05220e11i	−1.49386	−	0.862481i
$592$	−4.32261e10	−	2.49566e10i	−0.351933	−	0.203188i
$593$	−3.86450e10	−	6.69351e10i	−0.312518	−	0.541296i	0.666389	−	0.745604i	$-0.267839\pi$
$593$	−3.86450e10	−	6.69351e10i	−0.312518	−	0.541296i	−0.978907	+	0.204308i	$0.934506\pi$
$594$	−1.14739e10	+	1.98733e10i	−0.0921645	+	0.159634i
$595$	−1.55415e10	−	2.69187e10i	−0.124001	−	0.214776i
$596$	3.16488e10			0.250826
$597$			3.66467e11i			2.88494i
$598$	1.46516e10	+	2.53773e10i	0.114572	+	0.198445i
$599$	−2.54280e10	+	1.46809e10i	−0.197517	+	0.114037i	−0.595497	−	0.803358i	$-0.703045\pi$
$599$	−2.54280e10	+	1.46809e10i	−0.197517	+	0.114037i	0.397980	+	0.917394i	$0.369711\pi$
$600$	−9.53975e9			−0.0736091
$601$		−	6.09708e10i		−	0.467330i	−0.972317	−	0.233665i	$-0.924928\pi$
$601$		−	6.09708e10i		−	0.467330i	0.972317	−	0.233665i	$-0.0750720\pi$
$602$	−5.58380e9	+	3.22381e9i	−0.0425152	+	0.0245462i
$603$	−2.60056e11	−	1.50144e11i	−1.96697	−	1.13563i
$604$	−5.20346e10	+	3.00422e10i	−0.390971	+	0.225727i
$605$	−5.21464e10	+	9.03201e10i	−0.389227	+	0.674160i
$606$	−8.78749e10	+	1.52204e11i	−0.651590	+	1.12859i
$607$			4.75299e10i			0.350116i	0.984558	+	0.175058i	$0.0560114\pi$
$607$			4.75299e10i			0.350116i	−0.984558	+	0.175058i	$0.943989\pi$
$608$	1.47285e10	−	1.91474e10i	0.107782	−	0.140118i
$609$	7.11555e9			0.0517296
$610$	9.16684e10	+	5.29248e10i	0.662065	+	0.382243i
$611$	8.75202e10	+	5.05298e10i	0.627977	+	0.362563i
$612$	−6.88924e10	−	1.19325e11i	−0.491095	−	0.850601i
$613$	−1.11178e10	+	1.92566e10i	−0.0787365	+	0.136376i	−0.902705	−	0.430260i	$-0.858422\pi$
$613$	−1.11178e10	+	1.92566e10i	−0.0787365	+	0.136376i	0.823969	+	0.566636i	$0.191755\pi$
$614$	8.89082e10	+	1.53994e11i	0.625559	+	1.08350i
$615$	1.06011e11			0.741053
$616$			4.16119e9i			0.0288998i
$617$	1.32351e11	+	2.29239e11i	0.913247	+	1.58179i	0.809448	+	0.587192i	$0.199766\pi$
$617$	1.32351e11	+	2.29239e11i	0.913247	+	1.58179i	0.103799	+	0.994598i	$0.466900\pi$
$618$	6.36204e10	−	3.67312e10i	0.436156	−	0.251815i
$619$	−1.35023e11			−0.919697			−0.459849	−	0.887997i	$-0.652096\pi$
$619$	−1.35023e11			−0.919697			−0.459849	+	0.887997i	$0.652096\pi$
$620$		−	1.80460e10i		−	0.122128i
$621$	−3.34311e10	+	1.93014e10i	−0.224793	+	0.129785i
$622$	5.43433e10	+	3.13751e10i	0.363065	+	0.209616i
$623$	3.17261e10	−	1.83171e10i	0.210603	−	0.121592i
$624$	−1.81221e10	+	3.13884e10i	−0.119528	+	0.207029i
$625$	8.52825e10	−	1.47714e11i	0.558908	−	0.968056i
$626$		−	8.25108e10i		−	0.537296i
$627$	−1.21434e11	−	1.61340e10i	−0.785721	−	0.104393i
$628$	8.77931e10			0.564445
$629$	−3.25732e11	−	1.88062e11i	−2.08093	−	1.20143i
$630$	−2.15070e10	−	1.24171e10i	−0.136527	−	0.0788239i
$631$	−8.44278e10	−	1.46233e11i	−0.532559	−	0.922420i	−0.999277	−	0.0380137i	$-0.987897\pi$
$631$	−8.44278e10	−	1.46233e11i	−0.532559	−	0.922420i	0.466718	−	0.884406i	$-0.345436\pi$
$632$	4.60654e10	−	7.97876e10i	0.288740	−	0.500112i
$633$	1.93265e10	+	3.34745e10i	0.120376	+	0.208497i
$634$	−1.33733e11			−0.827719
$635$		−	1.76023e11i		−	1.08262i
$636$	−8.68565e10	−	1.50440e11i	−0.530853	−	0.919464i
$637$	8.71329e10	−	5.03062e10i	0.529206	−	0.305537i
$638$	−1.31064e10			−0.0791042
$639$		−	5.33904e10i		−	0.320229i
$640$	−1.36904e10	+	7.90416e9i	−0.0816012	+	0.0471125i
$641$	−6.78466e10	−	3.91712e10i	−0.401879	−	0.232025i	0.285415	−	0.958404i	$-0.407869\pi$
$641$	−6.78466e10	−	3.91712e10i	−0.401879	−	0.232025i	−0.687295	+	0.726379i	$0.741202\pi$
$642$	4.60015e10	−	2.65590e10i	0.270790	−	0.156340i
$643$	−5.46118e10	+	9.45904e10i	−0.319479	+	0.553354i	−0.980379	−	0.197120i	$-0.936841\pi$
$643$	−5.46118e10	+	9.45904e10i	−0.319479	+	0.553354i	0.660900	+	0.750474i	$0.270175\pi$
$644$	−3.50000e9	+	6.06217e9i	−0.0203481	+	0.0352440i
$645$			1.24213e11i			0.717675i
$646$	1.10987e11	−	1.44286e11i	0.637299	−	0.828502i
$647$	6.38925e10			0.364613			0.182307	−	0.983242i	$-0.441644\pi$
$647$	6.38925e10			0.364613			0.182307	+	0.983242i	$0.441644\pi$
$648$	3.03920e10	+	1.75468e10i	0.172369	+	0.0995172i
$649$	6.35634e10	+	3.66983e10i	0.358285	+	0.206856i
$650$	5.39508e9	+	9.34454e9i	0.0302235	+	0.0523486i
$651$	4.94181e9	−	8.55946e9i	0.0275145	−	0.0476565i
$652$	4.28226e10	+	7.41709e10i	0.236964	+	0.410434i
$653$	1.66641e11			0.916495			0.458247	−	0.888825i	$-0.348477\pi$
$653$	1.66641e11			0.916495			0.458247	+	0.888825i	$0.348477\pi$
$654$		−	2.94289e11i		−	1.60866i
$655$	2.38566e9	+	4.13209e9i	0.0129612	+	0.0224494i
$656$	1.82638e10	−	1.05446e10i	0.0986224	−	0.0569397i
$657$	4.75824e11			2.55379
$658$			2.41413e10i			0.128783i
$659$	−2.25708e11	+	1.30312e11i	−1.19675	+	0.690946i	−0.959830	−	0.280583i	$-0.909472\pi$
$659$	−2.25708e11	+	1.30312e11i	−1.19675	+	0.690946i	−0.236923	+	0.971528i	$0.576139\pi$
$660$	6.94249e10	+	4.00825e10i	0.365881	+	0.211241i
$661$	−4.17938e10	+	2.41297e10i	−0.218930	+	0.126399i	−0.605455	−	0.795880i	$-0.707009\pi$
$661$	−4.17938e10	+	2.41297e10i	−0.218930	+	0.126399i	0.386525	+	0.922279i	$0.373675\pi$
$662$	2.13721e10	−	3.70176e10i	0.111280	−	0.192742i
$663$	−1.36560e11	+	2.36529e11i	−0.706755	+	1.22414i
$664$		−	1.81811e10i		−	0.0935291i
$665$	4.32122e9	−	3.25239e10i	0.0220963	−	0.166309i
$666$	−3.00509e11			−1.52743
$667$	−1.90938e10	−	1.10238e10i	−0.0964694	−	0.0556966i
$668$	7.32571e10	+	4.22950e10i	0.367912	+	0.212414i
$669$	1.56111e11	+	2.70392e11i	0.779343	+	1.34986i
$670$	−1.29809e11	+	2.24836e11i	−0.644179	+	1.11575i
$671$	−5.33910e10	−	9.24759e10i	−0.263377	−	0.456183i
$672$	−8.65808e9			−0.0424565
$673$		−	1.19906e11i		−	0.584496i	−0.956343	−	0.292248i	$-0.905597\pi$
$673$		−	1.19906e11i		−	0.584496i	0.956343	−	0.292248i	$-0.0944033\pi$
$674$	−9.98005e9	−	1.72859e10i	−0.0483607	−	0.0837633i
$675$	−1.23101e10	+	7.10726e9i	−0.0592991	+	0.0342363i
$676$	−6.34187e10			−0.303690
$677$			9.00557e10i			0.428703i	0.976757	+	0.214352i	$0.0687638\pi$
$677$			9.00557e10i			0.428703i	−0.976757	+	0.214352i	$0.931236\pi$
$678$	5.67851e10	−	3.27849e10i	0.268730	−	0.155151i
$679$	2.42505e10	+	1.40010e10i	0.114088	+	0.0658690i
$680$	−1.03165e11	+	5.95622e10i	−0.482498	+	0.278570i
$681$	4.19690e10	−	7.26925e10i	0.195137	−	0.337988i
$682$	−9.10248e9	+	1.57660e10i	−0.0420748	+	0.0728757i
$683$		−	5.87903e10i		−	0.270161i	−0.990835	−	0.135081i	$-0.956871\pi$
$683$		−	5.87903e10i		−	0.270161i	0.990835	−	0.135081i	$-0.0431293\pi$
$684$	1.91551e10	−	1.44172e11i	0.0875104	−	0.658653i
$685$	1.27765e11			0.580297
$686$	4.21576e10	+	2.43397e10i	0.190362	+	0.109905i
$687$	4.08305e11	+	2.35735e11i	1.83298	+	1.05827i
$688$	1.23551e10	+	2.13997e10i	0.0551433	+	0.0955111i
$689$	−9.82411e10	+	1.70159e11i	−0.435930	+	0.755052i
$690$	6.74272e10	+	1.16787e11i	0.297467	+	0.515228i
$691$	−3.43628e11			−1.50722			−0.753610	−	0.657321i	$-0.771689\pi$
$691$	−3.43628e11			−1.50722			−0.753610	+	0.657321i	$0.771689\pi$
$692$			1.25563e11i			0.547566i
$693$	1.25265e10	+	2.16965e10i	0.0543121	+	0.0940713i
$694$	−2.34633e11	+	1.35465e11i	−1.01147	+	0.583970i
$695$	−2.43303e11			−1.04282
$696$		−	2.72701e10i		−	0.116211i
$697$	1.37628e11	−	7.94593e10i	0.583142	−	0.336677i
$698$	−4.57590e10	−	2.64190e10i	−0.192777	−	0.111300i
$699$	5.85784e11	−	3.38203e11i	2.45374	−	1.41667i
$700$	−1.28879e9	+	2.23224e9i	−0.00536770	+	0.00929714i
$701$	5.61651e10	−	9.72808e10i	0.232592	−	0.402861i	−0.725978	−	0.687718i	$-0.758613\pi$
$701$	5.61651e10	−	9.72808e10i	0.232592	−	0.402861i	0.958570	+	0.284857i	$0.0919461\pi$
$702$			5.40050e10i			0.222375i
$703$	−1.51496e11	−	3.66977e11i	−0.620268	−	1.50251i
$704$	1.59476e10			0.0649239
$705$	4.02772e11	+	2.32540e11i	1.63043	+	0.941330i
$706$	−6.97376e10	−	4.02630e10i	−0.280704	−	0.162064i
$707$	2.37432e10	+	4.11244e10i	0.0950301	+	0.164597i
$708$	−7.63572e10	+	1.32255e11i	−0.303890	+	0.526354i
$709$	−1.66437e11	−	2.88278e11i	−0.658667	−	1.14084i	−0.980961	−	0.194205i	$-0.937787\pi$
$709$	−1.66437e11	−	2.88278e11i	−0.658667	−	1.14084i	0.322294	−	0.946640i	$-0.395546\pi$
$710$	−4.61597e10			−0.181648
$711$		−	5.54685e11i		−	2.17054i
$712$	−7.01994e10	−	1.21589e11i	−0.273158	−	0.473123i
$713$	−2.65216e10	+	1.53123e10i	−0.102622	+	0.0592491i
$714$	−6.52433e10			−0.251040
$715$		−	9.06725e10i		−	0.346938i
$716$	−1.90730e11	+	1.10118e11i	−0.725718	+	0.418994i
$717$	−1.08722e11	−	6.27709e10i	−0.411379	−	0.237510i
$718$	5.66766e10	−	3.27223e10i	0.213258	−	0.123125i
$719$	−1.90803e11	+	3.30480e11i	−0.713952	+	1.23660i	0.249410	+	0.968398i	$0.419763\pi$
$719$	−1.90803e11	+	3.30480e11i	−0.713952	+	1.23660i	−0.963362	+	0.268204i	$0.913570\pi$
$720$	−4.75880e10	+	8.24248e10i	−0.177079	+	0.306710i
$721$		−	1.98490e10i		−	0.0734511i
$722$	1.85718e11	−	4.92897e10i	0.683446	−	0.181388i
$723$	7.53494e11			2.75757
$724$	−8.44033e10	−	4.87302e10i	−0.307189	−	0.177355i
$725$	−7.03082e9	−	4.05925e9i	−0.0254480	−	0.0146924i
$726$	1.09455e11	+	1.89582e11i	0.393995	+	0.682419i
$727$	−1.22890e10	+	2.12853e10i	−0.0439927	+	0.0761976i	−0.887183	−	0.461417i	$-0.847341\pi$
$727$	−1.22890e10	+	2.12853e10i	−0.0439927	+	0.0761976i	0.843191	+	0.537615i	$0.180674\pi$
$728$	4.89646e9	+	8.48091e9i	0.0174324	+	0.0301938i
$729$	4.27606e11			1.51403
$730$		−	4.11382e11i		−	1.44862i
$731$	9.31025e10	+	1.61258e11i	0.326056	+	0.564745i
$732$	1.92412e11	−	1.11089e11i	0.670175	−	0.386926i
$733$	−8.87852e10			−0.307556			−0.153778	−	0.988105i	$-0.549144\pi$
$733$	−8.87852e10			−0.307556			−0.153778	+	0.988105i	$0.549144\pi$
$734$		−	4.95344e10i		−	0.170656i
$735$	4.00989e11	−	2.31511e11i	1.37399	−	0.793273i
$736$	2.32330e10	+	1.34136e10i	0.0791762	+	0.0457124i
$737$	2.26817e11	−	1.30953e11i	0.768787	−	0.443859i
$738$	6.34851e10	−	1.09959e11i	0.214016	−	0.370687i
$739$	−7.18850e10	+	1.24508e11i	−0.241024	+	0.417466i	−0.961006	−	0.276527i	$-0.910817\pi$
$739$	−7.18850e10	+	1.24508e11i	−0.241024	+	0.417466i	0.719982	+	0.693993i	$0.244150\pi$
$740$			2.59810e11i			0.866422i
$741$	−2.66478e11	+	1.10008e11i	−0.883871	+	0.364880i
$742$	−4.69360e10			−0.154843
$743$	−3.18339e10	−	1.83793e10i	−0.104456	−	0.0603078i	0.446862	−	0.894603i	$-0.352542\pi$
$743$	−3.18339e10	−	1.83793e10i	−0.104456	−	0.0603078i	−0.551318	+	0.834295i	$0.685875\pi$
$744$	−3.28038e10	−	1.89393e10i	−0.107061	−	0.0618118i
$745$	−8.23699e10	−	1.42669e11i	−0.267389	−	0.463131i
$746$	−5.40158e10	+	9.35581e10i	−0.174408	+	0.302083i
$747$	−5.47307e10	−	9.47963e10i	−0.175772	−	0.304445i
$748$	1.20174e11			0.383887
$749$		−	1.43521e10i		−	0.0456024i
$750$	−1.57160e11	−	2.72210e11i	−0.496705	−	0.860318i
$751$	−4.57004e11	+	2.63851e11i	−1.43668	+	0.829468i	−0.997618	−	0.0689878i	$-0.978023\pi$
$751$	−4.57004e11	+	2.63851e11i	−1.43668	+	0.829468i	−0.439064	+	0.898456i	$0.644690\pi$
$752$	9.25206e10			0.289312
$753$		−	2.84514e11i		−	0.884961i
$754$	−2.67121e10	+	1.54222e10i	−0.0826460	+	0.0477157i
$755$	2.70853e11	+	1.56377e11i	0.833576	+	0.481265i
$756$	−1.11724e10	+	6.45040e9i	−0.0342027	+	0.0197469i
$757$	−1.67939e11	+	2.90879e11i	−0.511409	+	0.885786i	0.488504	+	0.872562i	$0.337543\pi$
$757$	−1.67939e11	+	2.90879e11i	−0.511409	+	0.885786i	−0.999913	+	0.0132243i	$0.995790\pi$
$758$	6.44819e9	−	1.11686e10i	0.0195327	−	0.0338315i
$759$		−	1.36042e11i		−	0.409927i
$760$	−1.24647e11	−	1.65609e10i	−0.373617	−	0.0496397i
$761$	−2.33281e11			−0.695571			−0.347786	−	0.937574i	$-0.613066\pi$
$761$	−2.33281e11			−0.695571			−0.347786	+	0.937574i	$0.613066\pi$
$762$	−3.19973e11	−	1.84737e11i	−0.949060	−	0.547940i
$763$	−6.88619e10	−	3.97574e10i	−0.203180	−	0.117306i
$764$	−4.95321e10	−	8.57921e10i	−0.145383	−	0.251811i
$765$	−3.58602e11	+	6.21116e11i	−1.04705	+	1.81354i
$766$	1.46360e11	+	2.53504e11i	0.425117	+	0.736324i
$767$	1.72731e11			0.499102
$768$			3.31817e10i			0.0953792i
$769$	−1.45752e11	−	2.52450e11i	−0.416783	−	0.721889i	0.578831	−	0.815448i	$-0.303509\pi$
$769$	−1.45752e11	−	2.52450e11i	−0.416783	−	0.721889i	−0.995614	+	0.0935585i	$0.970176\pi$
$770$	1.87581e10	−	1.08300e10i	0.0533613	−	0.0308082i
$771$	−1.33001e11			−0.376389
$772$		−	1.69705e11i		−	0.477777i
$773$	−5.34393e11	+	3.08532e11i	−1.49673	+	0.864137i	−0.999993	−	0.00376506i	$-0.998802\pi$
$773$	−5.34393e11	+	3.08532e11i	−1.49673	+	0.864137i	−0.496736	+	0.867902i	$0.665468\pi$
$774$	1.28840e11	+	7.43855e10i	0.358992	+	0.207264i
$775$	−9.76592e9	+	5.63836e9i	−0.0270711	+	0.0156295i
$776$	5.36584e10	−	9.29390e10i	0.147976	−	0.256301i
$777$	−7.11479e10	+	1.23232e11i	−0.195199	+	0.338095i
$778$			3.39764e11i			0.927383i
$779$	1.66286e11	+	2.20932e10i	0.451549	+	0.0599940i
$780$	1.88660e11			0.509684
$781$	4.03276e10	+	2.32832e10i	0.108392	+	0.0625803i
$782$	1.75074e11	+	1.01079e11i	0.468159	+	0.270292i
$783$	−2.03166e10	−	3.51894e10i	−0.0540511	−	0.0936192i
$784$	4.60556e10	−	7.97706e10i	0.121904	−	0.211144i
$785$	−2.28492e11	−	3.95760e11i	−0.601718	−	1.04221i
$786$	1.00150e10			0.0262399
$787$			5.39551e11i			1.40648i	0.710952	+	0.703240i	$0.248264\pi$
$787$			5.39551e11i			1.40648i	−0.710952	+	0.703240i	$0.751736\pi$
$788$	1.08956e11	+	1.88717e11i	0.282583	+	0.489448i
$789$	−6.38752e11	+	3.68784e11i	−1.64825	+	0.951620i
$790$	−4.79563e11			−1.23122
$791$		−	1.77165e10i		−	0.0452555i
$792$	8.31509e10	−	4.80072e10i	0.211333	−	0.122013i
$793$	−2.17632e11	−	1.25650e11i	−0.550339	−	0.317738i
$794$	3.43395e11	−	1.98259e11i	0.863997	−	0.498829i
$795$	−4.52109e11	+	7.83076e11i	−1.13181	+	1.96036i
$796$	1.89739e11	−	3.28637e11i	0.472611	−	0.818586i
$797$		−	4.21660e11i		−	1.04503i	−0.852630	−	0.522515i	$-0.824994\pi$
$797$		−	4.21660e11i		−	1.04503i	0.852630	−	0.522515i	$-0.175006\pi$
$798$	−5.45865e10	−	4.19890e10i	−0.134609	−	0.103544i
$799$	6.97193e11			1.71067
$800$	8.55497e9	+	4.93922e9i	0.0208862	+	0.0120586i
$801$	−7.32041e11	−	4.22644e11i	−1.77830	−	1.02670i
$802$	1.82604e11	+	3.16280e11i	0.441381	+	0.764494i
$803$	−2.07503e11	+	3.59406e11i	−0.499071	+	0.864417i
$804$	2.72470e11	+	4.71932e11i	0.652071	+	1.12942i
$805$	3.64367e10			0.0867671
$806$			4.28434e10i			0.101518i
$807$	−5.98231e10	−	1.03617e11i	−0.141051	−	0.244307i
$808$	1.57607e11	−	9.09947e10i	0.369770	−	0.213487i
$809$	5.65745e11			1.32077			0.660384	−	0.750928i	$-0.270393\pi$
$809$	5.65745e11			1.32077			0.660384	+	0.750928i	$0.270393\pi$
$810$		−	1.82671e11i		−	0.424355i
$811$	−4.88868e11	+	2.82248e11i	−1.13008	+	0.652451i	−0.943955	−	0.330075i	$-0.892926\pi$
$811$	−4.88868e11	+	2.82248e11i	−1.13008	+	0.652451i	−0.186124	+	0.982526i	$0.559593\pi$
$812$	−6.38103e9	−	3.68409e9i	−0.0146780	−	0.00847434i
$813$	−5.11824e11	+	2.95502e11i	−1.17154	+	0.676391i
$814$	1.31050e11	−	2.26985e11i	0.298496	−	0.517010i
$815$	2.22902e11	−	3.86078e11i	0.505224	−	0.875073i
$816$			2.50042e11i			0.563966i
$817$	−2.58866e10	+	1.94837e11i	−0.0581013	+	0.437304i
$818$	−1.85387e10			−0.0414063
$819$	5.10604e10	+	2.94797e10i	0.113488	+	0.0655221i
$820$	−9.50674e10	−	5.48872e10i	−0.210270	−	0.121399i
$821$	4.09216e10	+	7.08783e10i	0.0900700	+	0.156006i	0.907540	−	0.419965i	$-0.137958\pi$
$821$	4.09216e10	+	7.08783e10i	0.0900700	+	0.156006i	−0.817470	+	0.575971i	$0.804624\pi$
$822$	1.34090e11	−	2.32250e11i	0.293703	−	0.508708i
$823$	1.09218e11	+	1.89170e11i	0.238064	+	0.412339i	0.960159	−	0.279455i	$-0.0901539\pi$
$823$	1.09218e11	+	1.89170e11i	0.238064	+	0.412339i	−0.722095	+	0.691794i	$0.756821\pi$
$824$	−7.60706e10			−0.165009
$825$		−	5.00941e10i		−	0.108136i
$826$	2.06312e10	+	3.57342e10i	0.0443204	+	0.0767652i
$827$	5.47020e11	−	3.15822e11i	1.16945	−	0.675182i	0.215899	−	0.976416i	$-0.430732\pi$
$827$	5.47020e11	−	3.15822e11i	1.16945	−	0.675182i	0.953550	+	0.301234i	$0.0973985\pi$
$828$	1.61516e11			0.343633
$829$		−	4.26142e11i		−	0.902270i	−0.892456	−	0.451135i	$-0.851019\pi$
$829$		−	4.26142e11i		−	0.902270i	0.892456	−	0.451135i	$-0.148981\pi$
$830$	−8.19579e10	+	4.73184e10i	−0.172695	+	0.0997052i
$831$	1.11960e11	+	6.46403e10i	0.234779	+	0.135550i
$832$	3.25027e10	−	1.87655e10i	0.0678308	−	0.0391621i
$833$	3.47054e11	−	6.01115e11i	0.720804	−	1.24847i
$834$	−2.55347e11	+	4.42273e11i	−0.527796	+	0.914169i
$835$		−	4.40311e11i		−	0.905762i
$836$	1.00545e11	+	7.73408e10i	0.205842	+	0.158338i
$837$	−5.64402e10			−0.114997
$838$	−3.19877e11	−	1.84681e11i	−0.648644	−	0.374495i
$839$	−3.48650e11	−	2.01293e11i	−0.703626	−	0.406238i	0.105071	−	0.994465i	$-0.466493\pi$
$839$	−3.48650e11	−	2.01293e11i	−0.703626	−	0.406238i	−0.808696	+	0.588226i	$0.799826\pi$
$840$	2.25337e10	+	3.90295e10i	0.0452601	+	0.0783927i
$841$	−2.38520e11	+	4.13128e11i	−0.476804	+	0.825849i
$842$	−6.01872e10	−	1.04247e11i	−0.119745	−	0.207404i
$843$	−4.97260e11			−0.984630
$844$		−	4.00253e10i		−	0.0788796i
$845$	1.65055e11	+	2.85884e11i	0.323744	+	0.560741i
$846$	4.82404e11	−	2.78516e11i	0.941736	−	0.543711i
$847$	5.91481e10			0.114923
$848$			1.79880e11i			0.347857i
$849$	1.02521e12	−	5.91904e11i	1.97325	−	1.13925i
$850$	6.44664e10	+	3.72197e10i	0.123497	+	0.0713012i
$851$	3.81836e11	−	2.20453e11i	0.728045	−	0.420337i
$852$	−4.84446e10	+	8.39086e10i	−0.0919364	+	0.159238i
$853$	2.21513e11	−	3.83671e11i	0.418410	−	0.724707i	−0.577370	−	0.816483i	$-0.695921\pi$
$853$	2.21513e11	−	3.83671e11i	0.418410	−	0.724707i	0.995780	+	0.0917754i	$0.0292542\pi$
$854$		−	6.00310e10i		−	0.112861i
$855$	−6.99763e11	+	2.88877e11i	−1.30944	+	0.540565i
$856$	−5.50038e10			−0.102447
$857$	−6.25553e11	−	3.61163e11i	−1.15969	−	0.669546i	−0.208458	−	0.978031i	$-0.566845\pi$
$857$	−6.25553e11	−	3.61163e11i	−1.15969	−	0.669546i	−0.951229	+	0.308485i	$0.900178\pi$
$858$	−1.64823e11	−	9.51608e10i	−0.304137	−	0.175594i
$859$	2.43695e11	+	4.22093e11i	0.447584	+	0.775238i	0.998228	−	0.0595020i	$-0.0189513\pi$
$859$	2.43695e11	+	4.22093e11i	0.447584	+	0.775238i	−0.550644	+	0.834740i	$0.685618\pi$
$860$	6.43114e10	−	1.11391e11i	0.117569	−	0.203636i
$861$	−3.00612e10	−	5.20676e10i	−0.0547008	−	0.0947447i
$862$	−5.61386e11			−1.01679
$863$		−	2.62231e11i		−	0.472759i	−0.971661	−	0.236380i	$-0.924039\pi$
$863$		−	2.62231e11i		−	0.472759i	0.971661	−	0.236380i	$-0.0759609\pi$
$864$	2.47209e10	+	4.28178e10i	0.0443618	+	0.0768369i
$865$	5.66021e11	−	3.26792e11i	1.01104	−	0.583723i
$866$	4.64521e11			0.825911
$867$			1.02192e12i			1.80859i
$868$	−8.86335e9	+	5.11726e9i	−0.0156142	+	0.00901484i
$869$	4.18972e11	+	2.41894e11i	0.734694	+	0.424176i
$870$	−1.22930e11	+	7.09736e10i	−0.214576	+	0.123885i
$871$	3.08184e11	−	5.33790e11i	0.535472	−	0.927465i
$872$	−1.52369e11	+	2.63910e11i	−0.263530	+	0.456447i
$873$		−	6.46114e11i		−	1.11238i
$874$	8.14254e10	+	1.97242e11i	0.139545	+	0.338028i
$875$	−8.49273e10			−0.144882
$876$	−7.47806e11	−	4.31746e11i	−1.26991	−	0.733182i
$877$	−4.82688e9	−	2.78680e9i	−0.00815958	−	0.00471094i	0.495915	−	0.868371i	$-0.334833\pi$
$877$	−4.82688e9	−	2.78680e9i	−0.00815958	−	0.00471094i	−0.504074	+	0.863660i	$0.668166\pi$
$878$	3.57811e11	+	6.19747e11i	0.602110	+	1.04288i
$879$	−1.20620e11	+	2.08919e11i	−0.202052	+	0.349964i
$880$	−4.15055e10	−	7.18897e10i	−0.0692110	−	0.119877i
$881$	−2.77594e11			−0.460793			−0.230397	−	0.973097i	$-0.574002\pi$
$881$	−2.77594e11			−0.460793			−0.230397	+	0.973097i	$0.574002\pi$
$882$		−	5.54567e11i		−	0.916388i
$883$	2.18383e11	+	3.78250e11i	0.359232	+	0.622209i	0.987833	−	0.155520i	$-0.0497052\pi$
$883$	2.18383e11	+	3.78250e11i	0.359232	+	0.622209i	−0.628600	+	0.777728i	$0.716372\pi$
$884$	2.44926e11	−	1.41408e11i	0.401075	−	0.231561i
$885$	7.94915e11			1.29583
$886$			6.49334e10i			0.105374i
$887$	1.64683e11	−	9.50799e10i	0.266045	−	0.153601i	−0.361044	−	0.932549i	$-0.617580\pi$
$887$	1.64683e11	−	9.50799e10i	0.266045	−	0.153601i	0.627089	+	0.778948i	$0.284246\pi$
$888$	4.72281e11	+	2.72671e11i	0.759536	+	0.438518i
$889$	−8.64544e10	+	4.99145e10i	−0.138414	+	0.0799134i
$890$	−3.65405e11	+	6.32900e11i	−0.582390	+	1.00873i
$891$	−9.21400e10	+	1.59591e11i	−0.146197	+	0.253220i
$892$		−	3.23307e11i		−	0.510687i
$893$	5.83314e11	+	4.48696e11i	0.917269	+	0.705580i
$894$	−3.45789e11			−0.541329
$895$	9.92798e11	+	5.73192e11i	1.54728	+	0.893322i
$896$	7.76432e9	+	4.48273e9i	0.0120468	+	0.00695521i
$897$	−1.60081e11	−	2.77268e11i	−0.247268	−	0.428281i
$898$	4.40535e11	−	7.63029e11i	0.677446	−	1.17337i
$899$	−1.61176e10	−	2.79166e10i	−0.0246753	−	0.0427389i
$900$	5.94743e10			0.0906483
$901$			1.35550e12i			2.05683i
$902$	5.53707e10	+	9.59049e10i	0.0836477	+	0.144882i
$903$	6.10076e10	−	3.52228e10i	0.0917557	−	0.0529752i
$904$	−6.78977e10			−0.101667
$905$			5.07306e11i			0.756267i
$906$	5.68520e11	−	3.28235e11i	0.843787	−	0.487161i
$907$	1.47876e11	+	8.53760e10i	0.218508	+	0.126156i	0.605259	−	0.796028i	$-0.293069\pi$
$907$	1.47876e11	+	8.53760e10i	0.218508	+	0.126156i	−0.386751	+	0.922184i	$0.626403\pi$
$908$	−7.52732e10	+	4.34590e10i	−0.110738	+	0.0639347i
$909$	5.47845e11	−	9.48895e11i	0.802421	−	1.38983i
$910$	2.54873e10	−	4.41452e10i	0.0371670	−	0.0643751i
$911$		−	9.50743e11i		−	1.38035i	−0.723642	−	0.690175i	$-0.757533\pi$
$911$		−	9.50743e11i		−	1.38035i	0.723642	−	0.690175i	$-0.242467\pi$
$912$	−1.60921e11	+	2.09201e11i	−0.232613	+	0.302401i
$913$	9.54706e10			0.137400
$914$	−7.22829e11	−	4.17325e11i	−1.03574	−	0.597984i
$915$	−1.00155e12	−	5.78246e11i	−1.42886	−	0.824952i
$916$	−2.44104e11	−	4.22801e11i	−0.346732	−	0.600557i
$917$	1.35299e9	−	2.34345e9i	0.00191346	−	0.00331420i
$918$	1.86285e11	+	3.22656e11i	0.262306	+	0.454327i
$919$	−1.05693e12			−1.48178			−0.740888	−	0.671628i	$-0.765595\pi$
$919$	−1.05693e12			−1.48178			−0.740888	+	0.671628i	$0.765595\pi$
$920$		−	1.39642e11i		−	0.194924i
$921$	−9.71395e11	−	1.68250e12i	−1.35007	−	2.33839i
$922$	7.53943e11	−	4.35289e11i	1.04331	−	0.602357i
$923$	1.09589e11			0.150994
$924$		−	4.54644e10i		−	0.0623711i
$925$	1.40601e11	−	8.11762e10i	0.192054	−	0.110882i
$926$	7.04324e11	+	4.06642e11i	0.957919	+	0.553055i
$927$	−3.96633e11	+	2.28996e11i	−0.537118	+	0.310105i
$928$	−1.41191e10	+	2.44550e10i	−0.0190377	+	0.0329743i
$929$	4.72602e11	−	8.18571e11i	0.634502	−	1.09899i	−0.352118	−	0.935955i	$-0.614539\pi$
$929$	4.72602e11	−	8.18571e11i	0.634502	−	1.09899i	0.986620	−	0.163034i	$-0.0521281\pi$
$930$			1.97167e11i			0.263574i
$931$	6.77229e11	−	2.79574e11i	0.901440	−	0.372133i
$932$	−7.00420e11			−0.928314
$933$	−5.93745e11	−	3.42799e11i	−0.783562	−	0.452390i
$934$	1.16849e11	+	6.74626e10i	0.153545	+	0.0886493i
$935$	−3.12767e11	−	5.41728e11i	−0.409236	−	0.708818i
$936$	1.12980e11	−	1.95687e11i	0.147197	−	0.254952i
$937$	2.86481e11	+	4.96200e11i	0.371653	+	0.643722i	0.989820	−	0.142325i	$-0.0454578\pi$
$937$	2.86481e11	+	4.96200e11i	0.371653	+	0.643722i	−0.618167	+	0.786047i	$0.712124\pi$
$938$	1.47239e11			0.190200
$939$			9.01497e11i			1.15958i
$940$	−2.40796e11	−	4.17071e11i	−0.308417	−	0.534193i
$941$	−3.84011e11	+	2.21709e11i	−0.489762	+	0.282764i	−0.724476	−	0.689300i	$-0.757918\pi$
$941$	−3.84011e11	+	2.21709e11i	−0.489762	+	0.282764i	0.234714	+	0.972064i	$0.424585\pi$
$942$	−9.59211e11			−1.21818
$943$			1.86290e11i			0.235583i
$944$	1.36950e11	−	7.90681e10i	0.172454	−	0.0995665i
$945$	5.81552e10	+	3.35759e10i	0.0729225	+	0.0421018i
$946$	−1.12372e11	+	6.48779e10i	−0.140311	+	0.0810088i
$947$	−2.00522e11	+	3.47315e11i	−0.249323	+	0.431840i	−0.963338	−	0.268290i	$-0.913541\pi$
$947$	−2.00522e11	+	3.47315e11i	−0.249323	+	0.431840i	0.714015	+	0.700130i	$0.246875\pi$
$948$	−5.03302e11	+	8.71744e11i	−0.623154	+	1.07933i
$949$			9.76673e11i			1.20416i
$950$	2.99829e10	+	7.26292e10i	0.0368111	+	0.0891696i
$951$	1.46115e12			1.78637
$952$	5.85084e10	+	3.37798e10i	0.0712312	+	0.0411253i
$953$	−8.29251e11	−	4.78768e11i	−1.00534	−	0.580435i	−0.0955185	−	0.995428i	$-0.530451\pi$
$953$	−8.29251e11	−	4.78768e11i	−1.00534	−	0.580435i	−0.909825	+	0.414992i	$0.863784\pi$
$954$	5.41496e11	+	9.37899e11i	0.653735	+	1.13230i
$955$	−2.57827e11	+	4.46569e11i	−0.309966	+	0.536877i
$956$	6.49994e10	+	1.12582e11i	0.0778176	+	0.134784i
$957$	1.43198e11			0.170722
$958$			1.10862e12i			1.31620i
$959$	−3.62301e10	−	6.27523e10i	−0.0428346	−	0.0741917i
$960$	1.49579e11	−	8.63594e10i	0.176111	−	0.101677i
$961$	8.08116e11			0.947502
$962$		−	6.16822e11i		−	0.720211i
$963$	−2.86791e11	+	1.65579e11i	−0.333472	+	0.192530i
$964$	−6.75712e11	−	3.90122e11i	−0.782444	−	0.451744i
$965$	−7.65008e11	+	4.41678e11i	−0.882179	+	0.509326i
$966$	3.82403e10	−	6.62342e10i	0.0439150	−	0.0760630i
$967$	−3.33325e11	+	5.77335e11i	−0.381208	+	0.660271i	−0.991235	−	0.132109i	$-0.957825\pi$
$967$	−3.33325e11	+	5.77335e11i	−0.381208	+	0.660271i	0.610028	+	0.792380i	$0.291158\pi$
$968$		−	2.26682e11i		−	0.258176i
$969$	−1.21263e12	+	1.57644e12i	−1.37541	+	1.78806i
$970$	−5.58610e11			−0.630988
$971$	1.42505e12	+	8.22751e11i	1.60307	+	0.925532i	0.990869	+	0.134830i	$0.0430488\pi$
$971$	1.42505e12	+	8.22751e11i	1.60307	+	0.925532i	0.612200	+	0.790703i	$0.290285\pi$
$972$	−5.26047e11	−	3.03713e11i	−0.589331	−	0.340251i
$973$	6.89928e10	+	1.19499e11i	0.0769755	+	0.133325i
$974$	−4.74797e11	+	8.22372e11i	−0.527560	+	0.913761i
$975$	−5.89456e10	−	1.02097e11i	−0.0652278	−	0.112978i
$976$	−2.30066e11			−0.253544
$977$			1.19532e12i			1.31191i	0.754799	+	0.655956i	$0.227734\pi$
$977$			1.19532e12i			1.31191i	−0.754799	+	0.655956i	$0.772266\pi$
$978$	−4.67872e11	−	8.10378e11i	−0.511413	−	0.885793i
$979$	6.38475e11	−	3.68624e11i	0.695045	−	0.401285i
$980$	−4.79461e11			−0.519815
$981$			1.83471e12i			1.98103i
$982$	2.77492e11	−	1.60210e11i	0.298404	−	0.172283i
$983$	1.20942e10	+	6.98260e9i	0.0129528	+	0.00747830i	0.506462	−	0.862262i	$-0.330953\pi$
$983$	1.20942e10	+	6.98260e9i	0.0129528	+	0.00747830i	−0.493510	+	0.869740i	$0.664286\pi$
$984$	−1.99547e11	+	1.15208e11i	−0.212845	+	0.122886i
$985$	5.67142e11	−	9.82318e11i	0.602486	−	1.04354i
$986$	−1.06395e11	+	1.84282e11i	−0.112568	+	0.194973i
$987$		−	2.63764e11i		−	0.277937i
$988$	2.95927e11	+	3.93176e10i	0.310568	+	0.0412629i
$989$	−2.18277e11			−0.228151
$990$	−4.32821e11	−	2.49889e11i	−0.450575	−	0.260140i
$991$	−6.10752e11	−	3.52618e11i	−0.633242	−	0.365603i	0.148764	−	0.988873i	$-0.452470\pi$
$991$	−6.10752e11	−	3.52618e11i	−0.633242	−	0.365603i	−0.782007	+	0.623270i	$0.785804\pi$
$992$	1.96117e10	+	3.39684e10i	0.0202520	+	0.0350775i
$993$	−2.33508e11	+	4.04447e11i	−0.240162	+	0.415972i
$994$	1.30894e10	+	2.26715e10i	0.0134083	+	0.0232239i
$995$	−1.97527e12			−2.01528
$996$			1.98643e11i			0.201853i
$997$	−7.33268e11	−	1.27006e12i	−0.742134	−	1.28541i	−0.951522	−	0.307581i	$-0.900481\pi$
$997$	−7.33268e11	−	1.27006e12i	−0.742134	−	1.28541i	0.209388	−	0.977833i	$-0.432853\pi$
$998$	1.06046e12	−	6.12256e11i	1.06899	−	0.617179i
$999$	8.12578e11			0.815836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.9.d.a.27.7	✓	24
19.12	odd	6	inner	38.9.d.a.31.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.9.d.a.27.7	✓	24	1.1	even	1	trivial
38.9.d.a.31.7	yes	24	19.12	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	38.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(9.79796 + 5.65685i) q^{2} +(-107.051 - 61.8057i) q^{3} +(64.0000 + 110.851i) q^{4} +(333.136 - 577.008i) q^{5} +(-699.252 - 1211.14i) q^{6} -377.866 q^{7} +1448.15i q^{8} +(4359.40 + 7550.70i) q^{9} +O(q^{10})\)	\(q+(9.79796 + 5.65685i) q^{2} +(-107.051 - 61.8057i) q^{3} +(64.0000 + 110.851i) q^{4} +(333.136 - 577.008i) q^{5} +(-699.252 - 1211.14i) q^{6} -377.866 q^{7} +1448.15i q^{8} +(4359.40 + 7550.70i) q^{9} +(6528.10 - 3769.00i) q^{10} -7604.40 q^{11} -15822.3i q^{12} +(-15498.5 + 8948.07i) q^{13} +(-3702.31 - 2137.53i) q^{14} +(-71324.8 + 41179.4i) q^{15} +(-8192.00 + 14189.0i) q^{16} +(-61731.2 + 106922. i) q^{17} +98641.9i q^{18} +(-120460. + 49728.5i) q^{19} +85282.7 q^{20} +(40450.8 + 23354.3i) q^{21} +(-74507.6 - 43017.0i) q^{22} +(-72363.6 - 125337. i) q^{23} +(89504.3 - 155026. i) q^{24} +(-26646.1 - 46152.3i) q^{25} -202472. q^{26} -266728. i q^{27} +(-24183.4 - 41886.9i) q^{28} +(131930. - 76169.7i) q^{29} -931783. q^{30} -211602. i q^{31} +(-160530. + 92681.9i) q^{32} +(814056. + 469996. i) q^{33} +(-1.20968e6 + 698409. i) q^{34} +(-125881. + 218031. i) q^{35} +(-558003. + 966490. i) q^{36} +3.04646e6i q^{37} +(-1.46157e6 - 194188. i) q^{38} +2.21217e6 q^{39} +(835596. + 482432. i) q^{40} +(-1.11473e6 - 643591. i) q^{41} +(264223. + 457649. i) q^{42} +(754096. - 1.30613e6i) q^{43} +(-486682. - 842958. i) q^{44} +5.80908e6 q^{45} -1.63740e6i q^{46} +(-2.82350e6 - 4.89045e6i) q^{47} +(1.75392e6 - 1.01263e6i) q^{48} -5.62202e6 q^{49} -602932. i q^{50} +(1.32167e7 - 7.63068e6i) q^{51} +(-1.98381e6 - 1.14535e6i) q^{52} +(9.50811e6 - 5.48951e6i) q^{53} +(1.50884e6 - 2.61339e6i) q^{54} +(-2.53330e6 + 4.38780e6i) q^{55} -547208. i q^{56} +(1.59688e7 + 2.12166e6i) q^{57} +1.72352e6 q^{58} +(-8.35876e6 - 4.82593e6i) q^{59} +(-9.12957e6 - 5.27096e6i) q^{60} +(7.02107e6 + 1.21608e7i) q^{61} +(1.19700e6 - 2.07327e6i) q^{62} +(-1.64727e6 - 2.85315e6i) q^{63} -2.09715e6 q^{64} +1.19237e7i q^{65} +(5.31739e6 + 9.21000e6i) q^{66} +(-2.98271e7 + 1.72207e7i) q^{67} -1.58032e7 q^{68} +1.78899e7i q^{69} +(-2.46674e6 + 1.42418e6i) q^{70} +(-5.30319e6 - 3.06180e6i) q^{71} +(-1.09346e7 + 6.31308e6i) q^{72} +(2.72872e7 - 4.72629e7i) q^{73} +(-1.72334e7 + 2.98491e7i) q^{74} +6.58752e6i q^{75} +(-1.32219e7 - 1.01705e7i) q^{76} +2.87344e6 q^{77} +(2.16747e7 + 1.25139e7i) q^{78} +(-5.50960e7 - 3.18097e7i) q^{79} +(5.45809e6 + 9.45369e6i) q^{80} +(1.21167e7 - 2.09867e7i) q^{81} +(-7.28141e6 - 1.26118e7i) q^{82} -1.25546e7 q^{83} +5.97870e6i q^{84} +(4.11297e7 + 7.12387e7i) q^{85} +(1.47772e7 - 8.53163e6i) q^{86} -1.88309e7 q^{87} -1.10124e7i q^{88} +(-8.39613e7 + 4.84751e7i) q^{89} +(5.69171e7 + 3.28611e7i) q^{90} +(5.85636e6 - 3.38117e6i) q^{91} +(9.26254e6 - 1.60432e7i) q^{92} +(-1.30782e7 + 2.26521e7i) q^{93} -6.38886e7i q^{94} +(-1.14359e7 + 8.60727e7i) q^{95} +2.29131e7 q^{96} +(-6.41775e7 - 3.70529e7i) q^{97} +(-5.50843e7 - 3.18029e7i) q^{98} +(-3.31506e7 - 5.74186e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 168 q^{3} + 1536 q^{4} - 558 q^{5} + 896 q^{6} + 11992 q^{7} + 18448 q^{9}+O(q^{10}) \) 24 * q + 168 * q^3 + 1536 * q^4 - 558 * q^5 + 896 * q^6 + 11992 * q^7 + 18448 * q^9	\( 24 q + 168 q^{3} + 1536 q^{4} - 558 q^{5} + 896 q^{6} + 11992 q^{7} + 18448 q^{9} + 33516 q^{11} + 60870 q^{13} - 71424 q^{14} - 351930 q^{15} - 196608 q^{16} + 3546 q^{17} - 727738 q^{19} - 142848 q^{20} - 674568 q^{21} - 681600 q^{22} + 726 q^{23} - 114688 q^{24} - 277874 q^{25} - 960000 q^{26} + 767488 q^{28} - 254286 q^{29} - 71168 q^{30} - 2796150 q^{33} - 2740224 q^{34} - 690672 q^{35} - 2361344 q^{36} - 6829056 q^{38} - 1599924 q^{39} - 5153976 q^{41} + 4153600 q^{42} + 5692338 q^{43} + 2145024 q^{44} + 42653840 q^{45} + 11113938 q^{47} - 2752512 q^{48} + 17359944 q^{49} + 62169786 q^{51} + 7791360 q^{52} + 10399050 q^{53} - 24215680 q^{54} + 40181572 q^{55} - 27798558 q^{57} - 10126848 q^{58} - 58809492 q^{59} - 45047040 q^{60} - 45012614 q^{61} + 5892096 q^{62} + 62488724 q^{63} - 50331648 q^{64} + 45107968 q^{66} - 93677268 q^{67} + 907776 q^{68} - 291840 q^{70} + 5993046 q^{71} + 11698176 q^{72} + 23359860 q^{73} - 31474944 q^{74} - 1303552 q^{76} + 35611680 q^{77} + 94099200 q^{78} - 93221166 q^{79} - 9142272 q^{80} - 115510580 q^{81} + 6074880 q^{82} - 194283156 q^{83} - 15300674 q^{85} + 58611456 q^{86} + 89779380 q^{87} - 49833126 q^{89} - 63377664 q^{90} - 101275308 q^{91} - 92928 q^{92} - 157549992 q^{93} - 87570126 q^{95} - 29360128 q^{96} - 178814556 q^{97} - 88409088 q^{98} - 54444376 q^{99}+O(q^{100}) \) 24 * q + 168 * q^3 + 1536 * q^4 - 558 * q^5 + 896 * q^6 + 11992 * q^7 + 18448 * q^9 + 33516 * q^11 + 60870 * q^13 - 71424 * q^14 - 351930 * q^15 - 196608 * q^16 + 3546 * q^17 - 727738 * q^19 - 142848 * q^20 - 674568 * q^21 - 681600 * q^22 + 726 * q^23 - 114688 * q^24 - 277874 * q^25 - 960000 * q^26 + 767488 * q^28 - 254286 * q^29 - 71168 * q^30 - 2796150 * q^33 - 2740224 * q^34 - 690672 * q^35 - 2361344 * q^36 - 6829056 * q^38 - 1599924 * q^39 - 5153976 * q^41 + 4153600 * q^42 + 5692338 * q^43 + 2145024 * q^44 + 42653840 * q^45 + 11113938 * q^47 - 2752512 * q^48 + 17359944 * q^49 + 62169786 * q^51 + 7791360 * q^52 + 10399050 * q^53 - 24215680 * q^54 + 40181572 * q^55 - 27798558 * q^57 - 10126848 * q^58 - 58809492 * q^59 - 45047040 * q^60 - 45012614 * q^61 + 5892096 * q^62 + 62488724 * q^63 - 50331648 * q^64 + 45107968 * q^66 - 93677268 * q^67 + 907776 * q^68 - 291840 * q^70 + 5993046 * q^71 + 11698176 * q^72 + 23359860 * q^73 - 31474944 * q^74 - 1303552 * q^76 + 35611680 * q^77 + 94099200 * q^78 - 93221166 * q^79 - 9142272 * q^80 - 115510580 * q^81 + 6074880 * q^82 - 194283156 * q^83 - 15300674 * q^85 + 58611456 * q^86 + 89779380 * q^87 - 49833126 * q^89 - 63377664 * q^90 - 101275308 * q^91 - 92928 * q^92 - 157549992 * q^93 - 87570126 * q^95 - 29360128 * q^96 - 178814556 * q^97 - 88409088 * q^98 - 54444376 * q^99

Introduction

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